Image-forming optical system

ABSTRACT

The present invention relates to a high-performance image-forming optical system made compact and thin by folding an optical path using reflecting surfaces arranged to minimize the number of reflections. A prism member  10  has a first entrance surface  11 , first to fourth reflecting surfaces  12  to  15 , and a first exit surface  16 . An optical path incident on the first reflecting surface  12  and an optical path reflected from the second reflecting surface  13  form intersecting optical paths. An optical path incident on the third reflecting surface  14  and an optical path reflected from the fourth reflecting surface  15  form intersecting optical paths. At least either one of the first reflecting surface  12  and the second reflecting surface  13  and at least either one of the third reflecting surface  14  and the fourth reflecting surface  15  have a rotationally asymmetric curved surface configuration that gives a power to a light beam and corrects aberrations due to decentration. An intermediate image plane is formed between the first reflecting surface  12  and the fourth reflecting surface  15.

CROSS REFERENCE TO RELATED APPLICATION

This application is a divisional of U.S. application Ser. No.09/501,320, filed Feb. 10, 2000, now abandoned the specification anddrawings of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates to image-forming optical systems. Moreparticularly, the present invention relates to a decentered opticalsystem with a reflecting surface having a power for use in opticalapparatus using a small-sized image pickup device, e.g. video cameras,digital still cameras, film scanners, and endoscopes.

Recently, with the achievement of small-sized image pickup devices,image-forming optical systems for use in video cameras, digital stillcameras, film scanners, endoscopes, etc. have also been demanded to bereduced in size and weight and also in cost.

In the general rotationally symmetric coaxial optical systems, however,optical elements are arranged in the direction of the optical axis.Therefore, there is a limit to the reduction in thickness of the opticalsystems. At the same time, the number of lens elements unavoidablyincreases because it is necessary to correct chromatic aberrationproduced by a rotationally symmetric refracting lens used in the opticalsystems. Therefore, it is difficult to reduce the cost in the presentstate of the art. Under these circumstances, there have recently beenproposed optical systems designed to be compact in size by giving apower to a reflecting surface, which produces no chromatic aberration,and folding an optical path in the optical axis direction.

Japanese Patent Application Unexamined Publication (KOKAI) Number[hereinafter referred to as “JP(A)”] 7-333505 proposes to reduce thethickness of an optical system by giving a power to a decenteredreflecting surface and thus folding an optical path. In an examplethereof, however, the number of constituent optical members is as largeas five, and actual optical performance is unclear. No mention is madeof the configuration of the reflecting surface.

JP(A) 8-292371, 9-5650 and 9-90229 each disclose an optical system inwhich an optical path is folded by a single prism or a plurality ofmirrors integrated into a single block, and an image is relayed in theoptical system to form a final image. In these conventional examples,however, the number of reflections increases because the image isrelayed. Accordingly, surface accuracy errors and decentration accuracyerrors are transferred while being added up. Consequently, the accuracyrequired for each surface becomes tight, causing the cost to increaseunfavorably. The relay of the image also causes the overall volumetriccapacity of the optical system to increase unfavorably.

JP(A) 9-222563 discloses an example of an optical system that uses aplurality of prisms. However, because the optical system is arranged torelay an image, the cost increases and the optical system becomes largein size unfavorably for the same reasons as stated above.

JP(A) 9-211331 discloses an example of an optical system in which anoptical path is folded by using a single prism to achieve a reduction insize of the optical system. However, the optical system is notsatisfactorily corrected for aberrations.

JP(A) 8-292368, 8-292372, 9-222561, 9-258105 and 9-258106 all discloseexamples of zoom lens systems. In these examples, however, the number ofreflections is undesirably large because an image is relayed in a prism.Therefore, surface accuracy errors and decentration accuracy errors ofreflecting surfaces are transferred while being added up, unfavorably.At the same time, the overall size of the optical system unavoidablyincreases, unfavorably.

JP(A) 10-20196 discloses an example of a two-unit zoom lens systemhaving a positive front unit and a negative rear unit, in which thepositive front unit comprises a prism of negative power placed on theobject side of a stop and a prism of positive power placed on the imageside of the stop. JP(A) 10-20196 also discloses an example in which thepositive front unit, which comprises a prism of negative power and aprism of positive power, is divided into two to form a three-unit zoomlens system having a negative unit, a positive unit and a negative unit.However, the prisms used in these examples each have two transmittingsurfaces and two reflecting surfaces, which are all independentsurfaces. Therefore, a relatively wide space must be ensured for theprisms. In addition, the image plane is large in size in conformity tothe Leica size film format. Accordingly, the prisms themselves becomeunavoidably large in size. Furthermore, because the disclosed zoom lenssystems are not telecentric on the image side, it is difficult to applythem to image pickup devices such as CCDs. In either of the examples ofzoom lens systems, zooming is performed by moving the prisms.Accordingly, the decentration accuracy required for the reflectingsurfaces becomes tight in order to maintain the required performanceover the entire zooming range, resulting in an increase in the cost.

When a general refracting optical system is used to obtain a desiredrefracting power, chromatic aberration occurs at an interface surfacethereof according to chromatic dispersion characteristics of an opticalelement. To correct the chromatic aberration and also correct other rayaberrations, the refracting optical system needs a large number ofconstituent elements, causing the cost to increase. In addition, becausethe optical path extends straight along the optical axis, the entireoptical system undesirably lengthens in the direction of the opticalaxis, resulting in an unfavorably large-sized image pickup apparatus.

In decentered optical systems such as those described above in regard tothe prior art, an imaged figure or the like is undesirably distorted andthe correct shape cannot be reproduced unless the formed image isfavorably corrected for aberrations, particularly rotationallyasymmetric distortion.

Furthermore, in a case where a reflecting surface is used in adecentered optical system, the sensitivity to decentration errors of thereflecting surface is twice as high as that in the case of a refractingsurface, and as the number of reflections increases, decentration errorsthat are transferred while being added up increase correspondingly.Consequently, manufacturing accuracy and assembly accuracy, e.g. surfaceaccuracy and decentration accuracy, required for reflecting surfacesbecome even more strict.

SUMMARY OF THE INVENTION

In view of the above-described problems with the prior art, an object ofthe present invention is to provide a high-performance and low-costimage-forming optical system having a reduced number of constituentoptical elements.

Another object of the present invention is to provide a high-performanceimage-forming optical system that is made compact and thin by folding anoptical path using reflecting surfaces arranged to minimize the numberof reflections.

The image-forming optical system according to the present inventionprovided to attain the above-described objects is an image-formingoptical system having a positive refracting power as a whole for formingan object image. The image-forming optical system has a prism memberformed from a medium having a refractive index (n) larger than 1 (n>1).The prism member has a first entrance surface through which a light beamfrom an object enters the prism member. The prism member further has afirst reflecting surface, a second reflecting surface, a thirdreflecting surface and a fourth reflecting surface, which reflect thelight beam in the prism member. Further, the prism member has a firstexit surface through which the light beam exits from the prism member.An optical path connecting the second reflecting surface and the thirdreflecting surface intersects an optical path connecting the firstentrance surface and the first reflecting surface, and the optical pathconnecting the second reflecting surface and the third reflectingsurface intersects an optical path connecting the fourth reflectingsurface and the first exit surface. At least either one of the firstreflecting surface and the second reflecting surface has a curvedsurface configuration that gives a power to a light beam. The curvedsurface configuration is a rotationally asymmetric surface configurationthat corrects aberrations due to decentration. At least either one ofthe third reflecting surface and the fourth reflecting surface has acurved surface configuration that gives a power to a light beam. Thecurved surface configuration is a rotationally asymmetric surfaceconfiguration that corrects aberrations due to decentration. Moreover,an intermediate image plane is formed between the first reflectingsurface and the fourth reflecting surface.

The reasons for adopting the above-described arrangement in the presentinvention, together with the function thereof, will be described belowin order.

The image-forming optical system according to the present invention,which is provided to attain the above-described objects, has a positiverefracting power as a whole for forming an object image. Theimage-forming optical system has a prism member formed from a mediumhaving a refractive index (n) larger than 1 (n>1). The prism member hasa first entrance surface through which a light beam from an objectenters the prism member. The prism member further has a first reflectingsurface, a second reflecting surface, a third reflecting surface and afourth reflecting surface, which reflect the light beam in the prismmember. Further, the prism member has a first exit surface through whichthe light beam exits from the prism member. An optical path connectingthe second reflecting surface and the third reflecting surfaceintersects an optical path connecting the first entrance surface and thefirst reflecting surface, and the optical path connecting the secondreflecting surface and the third reflecting surface intersects anoptical path connecting the fourth reflecting surface and the first exitsurface.

A refracting optical element such as a lens is provided with a power bygiving a curvature to an interface surface thereof. Accordingly, whenrays are refracted at the interface surface of the lens, chromaticaberration unavoidably occurs according to chromatic dispersioncharacteristics of the refracting optical element. Consequently, thecommon practice is to add another refracting optical element for thepurpose of correcting the chromatic aberration.

Meanwhile, a reflecting optical element such as a mirror or a prismproduces no chromatic aberration in theory even when a reflectingsurface thereof is provided with a power, and need not add anotheroptical element only for the purpose of correcting chromatic aberration.Accordingly, an optical system using a reflecting optical element allowsthe number of constituent optical elements to be reduced from theviewpoint of chromatic aberration correction in comparison to an opticalsystem using a refracting optical element.

At the same time, a reflecting optical system using a reflecting opticalelement allows the optical system itself to be compact in size incomparison to a refracting optical system because the optical path isfolded in the reflecting optical system.

Reflecting surfaces require a high degree of accuracy for assembly andadjustment because they have high sensitivity to decentration errors incomparison to refracting surfaces. However, among reflecting opticalelements, prisms, in which the positional relationship between surfacesis fixed, only need to control decentration as a single unit of prismand do not need high assembly accuracy and a large number of man-hoursfor adjustment as are needed for other reflecting optical elements.

Furthermore, a prism has an entrance surface and an exit surface, whichare refracting surfaces, and a reflecting surface. Therefore, the degreeof freedom for aberration correction is high in comparison to a mirror,which has only a reflecting surface. In particular, if the prismreflecting surface is assigned the greater part of the desired power tothereby reduce the powers of the entrance and exit surfaces, which arerefracting surfaces, it is possible to reduce chromatic aberration to avery small quantity in comparison to refracting optical elements such aslenses while maintaining the degree of freedom for aberration correctionat a high level in comparison to mirrors. Furthermore, the inside of aprism is filled with a transparent medium having a refractive indexhigher than that of air. Therefore, it is possible to obtain a longeroptical path length than in the case of air. Accordingly, the use of aprism makes it possible to obtain an optical system that is thinner andmore compact than those formed from lenses, mirrors and so forth, whichare placed in the air.

In the present invention, a prism member comprising one or twodecentered prisms is placed, and an object-side portion and image-sideportion of the prism member are arranged to correct each other'sdecentration aberrations, thereby enabling not only axial aberrationsbut also off-axis aberrations to be favorably corrected. If the numberof reflections is one in each of the portions, it is impossible tocorrect decentration aberrations completely.

For the reasons stated above, the present invention is arranged so thata light beam is reflected four times in the prism member, and anintermediate image plane is formed in an optical path between the firstreflecting surface and the fourth reflecting surface.

In the present invention, it is important that the axial principal rayshould intersect itself twice in the prism (which may be a singleintegral prism or a combination of two separate prisms). If the axialprincipal ray substantially intersects itself twice in the opticalsystem, the optical system can be folded so as to be compact in size.

The object-side portion of the prism member in the present invention hasa first entrance surface, a first reflecting surface and a secondreflecting surface and is arranged so that an optical path connectingthe second reflecting surface and a third reflecting surface intersectsan optical path connecting the first entrance surface and the firstreflecting surface.

The prism object-side portion having such a configuration enables anincrease in the degree of freedom for aberration correction and producesminimal aberrations. In addition, because the two reflecting surfaces ofthe prism object-side portion (i.e. the first reflecting surface and thesecond reflecting surface) can be positioned with a high degree ofsymmetry, aberrations produced by the two reflecting surfaces arecorrected with these reflecting surfaces by canceling the aberrationseach other. Therefore, the amount of aberration produced in the prismobject-side portion is small. Furthermore, because the optical pathsintersect each other in the prism object-side portion, the optical pathlength can be made long in comparison to a prism structure in which theoptical path is simply folded. Accordingly, the prism object-sideportion can be made compact in size, considering its optical pathlength. It is more desirable that the two reflecting surfaces in theprism object-side portion should have powers of different signs. Bydoing so, it is possible to enhance the effect of correcting eachother's aberrations by the two reflecting surfaces and hence possible toobtain high resolution.

In addition, if the prism object-side portion is formed by using a prismstructure in which the optical paths intersect each other as statedabove, it is possible to construct the prism object-side portion in acompact form. The reason for this is as follows. In a comparison betweenthe prism structure of the present invention and a prism structure ofthe same two-reflection type which has the same optical path length asthat of the above-described prism structure and in which a Z-shapedoptical path is formed, the prism structure of the present inventionprovides a higher space utilization efficiency. In the prismconfiguration having a Z-shaped optical path, rays invariably travelthrough different regions of the prism one by one, whereas in the prismin which the optical paths intersect each other, rays pass through thesame region twice. Accordingly, the prism can be made compact in size.

The image-side (image-formation plane-side) portion of the prism memberin the present invention has a third reflecting surface, a fourthreflecting surface and a first exit surface and is arranged so that theoptical path connecting the second reflecting surface and the thirdreflecting surface intersects an optical path connecting the fourthreflecting surface and the first exit surface.

The arrangement of the prism image-side portion is similar to thearrangement of the above-described prism object-side portion. Thus, theprism image-side portion similarly enables an increase in the degree offreedom for aberration correction and produces minimal aberrations. Inaddition, because the two reflecting surfaces of the prism image-sideportion (i.e. the third reflecting surface and the fourth reflectingsurface) can be positioned with a high degree of symmetry, aberrationsproduced by the two reflecting surfaces are corrected with thesereflecting surfaces by canceling the aberrations each other. Therefore,the amount of aberration produced in the prism image-side portion issmall. Furthermore, because the optical paths intersect each other inthe prism image-side portion, the optical path length can be made longin comparison to a prism structure in which the optical path is simplyfolded. Accordingly, the prism image-side portion can be made compact insize, considering its optical path length. It is more desirable that thetwo reflecting surfaces in the prism image-side portion should havepowers of different signs. By doing so, it is possible to enhance theeffect of correcting each other's aberrations by the two reflectingsurfaces and hence possible to obtain high resolution.

In addition, if the prism image-side portion is formed by using a prismstructure in which the optical paths intersect each other as statedabove, it is possible to construct the prism image-side portion in acompact form. The reason for this is as follows. In a comparison betweenthe prism structure of the present invention and a prism structure ofthe same two-reflection type which has the same optical path length asthat of the above-described prism structure and in which a Z-shapedoptical path is formed, the prism structure of the present inventionprovides a higher space utilization efficiency. In the prismconfiguration having a Z-shaped optical path, rays invariably travelthrough different regions of the prism one by one, whereas in the prismin which the optical paths intersect each other, rays pass through thesame region twice. Accordingly, the prism can be made compact in size.

Incidentally, in the present invention, the prism member may be formedfrom a combination of prisms cemented together or a single prismproduced by integral molding. It is also possible to form the prismmember from a combination of a first prism constituting the prismobject-side portion and a second prism constituting the prism image-sideportion.

When a light ray from the object center that passes through the centerof the stop and reaches the center of the image plane is defined as anaxial principal ray, if at least one reflecting surface of theobject-side portion of the prism member in the present invention and atleast one reflecting surface of the image-side portion of the prismmember are not decentered with respect to the axial principal ray, theaxial principal ray travels along the same optical path when incident onand reflected from each of the reflecting surfaces, and thus the axialprincipal ray is intercepted in the optical system undesirably. As aresult, an image is formed from only a light beam whose central portionis shaded. Consequently, the center of the image is unfavorably dark, orno image is formed in the center of the image field.

In addition, at least either one of the first reflecting surface and thesecond reflecting surface of the object-side portion of the prism memberin the present invention has a curved surface configuration that gives apower to a light beam, and the curved surface configuration is arotationally asymmetric surface configuration that corrects aberrationsdue to decentration. Moreover, at least either one of the thirdreflecting surface and the fourth reflecting surface of the image-sideportion of the prism member has a curved surface configuration thatgives a power to a light beam, and the curved surface configuration is arotationally asymmetric surface configuration that corrects aberrationsdue to decentration.

The reasons for adopting the above-described arrangements will bedescribed below in detail.

First, a coordinate system used in the following description androtationally asymmetric surfaces will be described.

An optical axis defined by a straight line along which the axialprincipal ray travels until it intersects the first surface of theoptical system is defined as a Z-axis. An axis perpendicularlyintersecting the Z-axis in the decentration plane of each surfaceconstituting the imaging optical system is defined as a Y-axis. An axisperpendicularly intersecting the optical axis and also perpendicularlyintersecting the Y-axis is defined as an X-axis. Ray tracing is forwardray tracing in which rays are traced from the object toward the imageplane.

In general, a spherical lens system comprising only a spherical lens isarranged such that aberrations produced by spherical surfaces, such asspherical aberration, coma and curvature of field, are corrected withsome surfaces by canceling the aberrations with each other, therebyreducing aberrations as a whole.

On the other hand, rotationally symmetric aspherical surfaces and thelike are used to correct aberrations favorably with a minimal number ofsurfaces. The reason for this is to reduce various aberrations thatwould be produced by spherical surfaces.

However, in a decentered optical system, rotationally asymmetricaberrations due to decentration cannot be corrected by a rotationallysymmetric optical system. Rotationally asymmetric aberrations due todecentration include distortion, curvature of field, and astigmatic andcomatic aberrations, which occur even on the axis.

First, rotationally asymmetric curvature of field will be described. Forexample, when rays from an infinitely distant object point are incidenton a decentered concave mirror, the rays are reflected by the concavemirror to form an image. In this case, the back focal length from thatportion of the concave mirror on which the rays strike to the imagesurface is a half the radius of curvature of the portion on which therays strike in a case where the medium on the image side is air.Consequently, as shown in FIG. 17, an image surface tilted with respectto the axial principal ray is formed. It is impossible to correct suchrotationally asymmetric curvature of field by a rotationally symmetricoptical system.

To correct the tilted curvature of field by the concave mirror M itself,which is the source of the curvature of field, the concave mirror M isformed from a rotationally asymmetric surface, and, in this example, theconcave mirror M is arranged such that the curvature is made strong(refracting power is increased) in the positive direction of the Y-axis,whereas the curvature is made weak (refracting power is reduced) in thenegative direction of the Y-axis. By doing so, the tilted curvature offield can be corrected. It is also possible to obtain a flat imagesurface with a minimal number of constituent surfaces by placing arotationally asymmetric surface having the same effect as that of theabove-described arrangement in the optical system separately from theconcave mirror M.

It is preferable that the rotationally asymmetric surface should be arotationally asymmetric surface having no axis of rotational symmetry inthe surface nor out of the surface. If the rotationally asymmetricsurface has no axis of rotational symmetry in the surface nor out of thesurface, the degree of freedom increases, and this is favorable foraberration correction.

Next, rotationally asymmetric astigmatism will be described.

A decentered concave mirror M produces astigmatism even for axial rays,as shown in FIG. 18, as in the case of the above. The astigmatism can becorrected by appropriately changing the curvatures in the X- and Y-axisdirections of the rotationally asymmetric surface as in the case of theabove.

Rotationally asymmetric coma will be described below.

A decentered concave mirror M produces coma even for axial rays, asshown in FIG. 19, as in the case of the above. The coma can be correctedby changing the tilt of the rotationally asymmetric surface according asthe distance from the origin of the X-axis increases, and furtherappropriately changing the tilt of the surface according to the sign(positive or negative) of the Y-axis.

The image-forming optical system according to the present invention mayalso be arranged such that the above-described at least one surfacehaving a reflecting action is decentered with respect to the axialprincipal ray and has a rotationally asymmetric surface configurationand further has a power. By adopting such an arrangement, decentrationaberrations produced as the result of giving a power to the reflectingsurface can be corrected by the surface itself. In addition, the powerof the refracting surfaces of the prism is reduced, and thus chromaticaberration produced in the prism can be minimized.

The above-described rotationally asymmetric surface used in the presentinvention should preferably be a plane-symmetry free-form surface havingonly one plane of symmetry. Free-form surfaces used in the presentinvention are defined by the following equation (a). It should be notedthat the Z-axis of the defining equation is the axis of a free-formsurface. $\begin{matrix}{Z = {{c\quad{r^{2}/\left\lbrack {1 + \sqrt{\left\{ {1 - {\left( {1 + k} \right)c^{2}r^{2}}} \right\}}} \right\rbrack}} + {\sum\limits_{j = 2}^{66}{C_{j}X^{m}Y^{n}}}}} & (a)\end{matrix}$

In Eq. (a), the first term is a spherical surface term, and the secondterm is a free-form surface term.

In the spherical surface term:

-   -   c: the curvature at the vertex    -   k: a conic constant    -   r=√{square root over ( )} (X²+Y²)

The free-form surface term is given by${\sum\limits_{j = 2}^{66}{C_{j}X^{m}Y^{n}}} = {{C_{2}X} + {C_{3}Y} + {C_{4}X^{2}} + {C_{5}X\quad Y} + {C_{6}Y^{2}} + {C_{7}X^{3}} + {C_{8}X^{2}Y} + {C_{9}X\quad Y^{2}} + {C_{10}Y^{3}} + {C_{11}X^{4}} + {C_{12}X^{3}Y} + {C_{13}X^{2}Y^{2}} + {C_{14}X\quad Y^{3}} + {C_{15}Y^{4}} + {C_{16}X^{5}} + {C_{17}X^{4}Y} + {C_{18}X^{3}Y^{2}} + {C_{19}X^{2}Y^{3}} + {C_{20}X\quad Y^{4}} + {C_{21}Y^{5}} + {C_{22}X^{6}} + {C_{23}X^{5}Y} + {C_{24}X^{4}Y^{2}} + {C_{25}X^{3}Y^{3}} + {C_{26}X^{2}Y^{4}} + {C_{27}X\quad Y^{5}} + {C_{28}Y^{6}} + {C_{29}X^{7}} + {C_{30}X^{6}Y} + {C_{31}X^{5}Y^{2}} + {C_{32}X^{4}Y^{3}} + {C_{33}X^{3}Y^{4}} + {C_{34}X^{2}Y^{5}} + {C_{35}X\quad Y^{6}} + {C_{36}Y^{7}\quad\cdots}}$where C_(j) (j is an integer of 2 or higher) are coefficients.

In general, the above-described free-form surface does not have planesof symmetry in both the XZ- and YZ-planes. In the present invention,however, a free-form surface having only one plane of symmetry parallelto the YZ-plane is obtained by making all terms of odd-numbered degreeswith respect to X zero. For example, in the above defining equation (a),the coefficients of the terms C₂, C₅, C₇, C₉, C₁₂, C₁₄, C₁₆, C₁₈, C₂₀,C₂₃, C₂₅, C₂₇, C₂₉, C₃₁, C₃₃, C₃₅, . . . are set equal to zero. By doingso, it is possible to obtain a free-form surface having only one planeof symmetry parallel to the YZ-plane.

A free-form surface having only one plane of symmetry parallel to theXZ-plane is obtained by making all terms of odd-numbered degrees withrespect to Y zero. For example, in the above defining equation (a), thecoefficients of the terms C₃, C₅, C₈, C₁₀, C₁₃, C₁₄, C₁₇, C₁₉, C₂₁, C₂₃,C₂₅, C₂₇, C₃₀, C₃₂, C₃₄, C₃₆, . . . are set equal to zero. By doing so,it is possible to obtain a free-form surface having only one plane ofsymmetry parallel to the XZ-plane.

Furthermore, the direction of decentration is determined incorrespondence to either of the directions of the above-described planesof symmetry. For example, with respect to the plane of symmetry parallelto the YZ-plane, the direction of decentration of the optical system isdetermined to be the Y-axis direction. With respect to the plane ofsymmetry parallel to the XZ-plane, the direction of decentration of theoptical system is determined to be the X-axis direction. By doing so,rotationally asymmetric aberrations due to decentration can be correctedeffectively, and at the same time, productivity can be improved.

It should be noted that the above defining equation (a) is shown asmerely an example, and that the feature of the present invention residesin that rotationally asymmetric aberrations due to decentration arecorrected and, at the same time, productivity is improved by using arotationally asymmetric surface having only one plane of symmetry.Therefore, the same advantageous effect can be obtained for any otherdefining equation that expresses such a rotationally asymmetric surface.

The image-forming optical system according to the present invention isan intermediate image formation type image-forming optical system inwhich an intermediate image plane is formed between the first reflectingsurface and the fourth reflecting surface. By the first entrancesurface, the first reflecting surface and the second reflecting surface,a light beam is rotated along a triangular path, thereby forming firstintersecting optical paths. By the third reflecting surface, the fourthreflecting surface and the first exit surface, a light beam is rotatedalong a triangular path, thereby forming second intersecting opticalpaths. The direction of rotation of the light beam traveling along thetriangular path to form the first intersecting optical paths and thedirection of rotation of the light beam traveling along the triangularpath to form the second intersecting optical paths may be either thesame or opposite to each other. The planes of rotation of the lightbeams may not extend parallel to each other but intersect each other, asa matter of course.

It is desirable that both the first reflecting surface and the secondreflecting surface should have a curved surface configuration that givesa power to a light beam, and the curved surface configuration should bea rotationally asymmetric surface configuration that correctsaberrations due to decentration.

It is desirable for both the third reflecting surface and the fourthreflecting surface to have a rotationally asymmetric surfaceconfiguration that gives a power to a light beam and correctsaberrations due to decentration.

It is desirable for the first entrance surface to have a rotationallyasymmetric surface configuration that gives a power to a light beam andcorrects aberrations due to decentration.

It is desirable for the first exit surface to have a rotationallyasymmetric surface configuration that gives a power to a light beam andcorrects aberrations due to decentration.

In the above, it is desirable that the rotationally asymmetric surfaceconfiguration should be a plane-symmetry free-form surface having onlyone plane of symmetry.

In this case, the one and only plane of symmetry of the plane-symmetryfree-form surface may be coincident with a plane formed by the axialprincipal ray traveling along the first intersecting optical paths.

The one and only plane of symmetry of the plane-symmetry free-formsurface may be coincident with a plane formed by the axial principal raytraveling along the second intersecting optical paths.

The intermediate image plane may be formed between the second reflectingsurface and the third reflecting surface.

In this case, it is desirable that the optical surfaces of the prismmember that are closer to the object side than the intermediate imageplane should be arranged to correct decentration aberrations as a wholeand the optical surfaces of the prism member that are closer to theimage-formation plane side than the intermediate image plane should bearranged to correct decentration aberrations as a whole so that theintermediate image plane is formed in an approximately planar shape.

Let us define the power of a decentered optical system and that of adecentered optical surface. As shown in FIG. 20, when the direction ofdecentration of a decentered optical system S is taken in the Y-axisdirection, a light ray which is parallel to the axial principal ray ofthe decentered optical system S and which has a small height d in theYZ-plane is made to enter the decentered optical system S from theobject side thereof. The angle that is formed between that ray and theaxial principal ray exiting from the decentered optical system S as thetwo rays are projected onto the YZ-plane is denoted by δy, and δy/d isdefined as the power Py in the Y-direction of the decentered opticalsystem S. A light ray which is parallel to the axial principal ray ofthe decentered optical system and which has a small height d in theX-direction, which is perpendicular to the YZ-plane, is made to enterthe decentered optical system from the object side thereof. The anglethat is formed between that ray and the axial principal ray exiting fromthe decentered optical system S as the two rays are projected onto aplane perpendicularly intersecting the YZ-plane and containing the axialprincipal ray is denoted by δx, and δx/d is defined as the power Px inthe X-direction of the decentered optical system S. The power Pyn in theY-direction and power Pxn in the X-direction of a decentered opticalsurface n constituting the decentered optical system S are defined inthe same way as the above.

Furthermore, the reciprocals of the above-described powers are definedas the focal length Fy in the Y-direction of the decentered opticalsystem, the focal length Fx in the X-direction of the decentered opticalsystem, the focal length Fyn in the Y-direction of the decenteredoptical surface n, and the focal length Fxn in the X-direction of thedecentered optical surface n, respectively.

When the powers in the X- and Y-directions of the two reflectingsurfaces (the first reflecting surface and the second reflectingsurface) of the prism object-side portion that form intersecting opticalpaths are denoted by Px1-1, Py1-1, Px1-2 and Py1-2, respectively, inorder from the object side, and the powers in the X- and Y-directions ofthe entire optical system are denoted by Px and Py, respectively, it isimportant to satisfy the following condition:0.4<Px1-1/Px<1.1  (1)

This condition defines the ratio of the power in the X-direction of thefirst reflecting surface to the power in the X-direction of the entiresystem. If Px1-1/Px is not larger than the lower limit, i.e. 0.4, thepositive power of the first reflecting surface becomes excessivelysmall, and it becomes necessary to assign a positive power to anothersurface. Consequently, the aberration correcting performance degrades.If Px1-1/Px is not smaller than the upper limit, i.e. 1.1, the positivepower assigned to the first reflecting surface becomes excessivelystrong. Consequently, decentration aberrations produced by this surfacebecome excessively large and hence difficult to correct by anothersurface.

It is even more desirable to satisfy the following condition:0.6<Px1-1/Px<1.0  (1-1)

Next, it is preferable to satisfy the following condition:0.1<Px1-2/Px<0.6  (2)

This condition defines the ratio of the power in the X-direction of thesecond reflecting surface to the power in the X-direction of the entiresystem. If Px1-2/Px is not larger than the lower limit, i.e. 0.1, thepositive power of the second reflecting surface becomes excessivelysmall, and it becomes necessary to assign a positive power to anothersurface. Consequently, the aberration correcting performance degrades.If Px1-2/Px is not smaller than the upper limit, i.e. 0.6, the positivepower assigned to the second reflecting surface becomes excessivelystrong. Consequently, decentration aberrations produced by this surfacebecome excessively large and hence difficult to correct by anothersurface.

It is even more desirable to satisfy the following condition:0.1<Px1-2/Px<0.4  (2-1)

When the powers in the X- and Y-directions of the two reflectingsurfaces (the third reflecting surface and the fourth reflectingsurface) of the prism image-side portion that form intersecting opticalpaths are denoted by Px2-1, Py2-1, Px2-2 and Py2-2, respectively, inorder from the object side, and the powers in the X- and Y-directions ofthe entire optical system are denoted by Px and Py, respectively, it ispreferable to satisfy the following condition:0.2<Px2-1/Px<1  (3)

This condition defines the ratio of the power in the X-direction of thethird reflecting surface to the power in the X-direction of the entiresystem. If Px2-1/Px is not larger than the lower limit, i.e. 0.2, thepositive power of the third reflecting surface becomes excessivelysmall, and it becomes necessary to assign a positive power to anothersurface. Consequently, the aberration correcting performance degrades.If Px2-1/Px is not smaller than the upper limit, i.e. 1, the positivepower assigned to the third reflecting surface becomes excessivelystrong. Consequently, decentration aberrations produced by this surfacebecome excessively large and hence difficult to correct by anothersurface.

It is even more desirable to satisfy the following condition:0.2<Px2-1/Px<0.8  (3-1)

It is still more desirable to satisfy all the above-described conditionsfrom the viewpoint of favorably correcting aberrations.

When the ratio of the power Px2-1 in the X-direction to the power Py2-1in the Y-direction of the third reflecting surface is expressed byPx2-1/Py2-1, it is preferable to satisfy the following condition:0.5<Px2-1/Py2-1<2.0  (4)

This condition defines the ratio of the power in the X-direction to thepower in the Y-direction of the third reflecting surface. If Px2-1/Py2-1is not larger than the lower limit, i.e. 0.5, the power in theX-direction becomes excessively small with respect to the power in theY-direction. Consequently, large astigmatic aberrations due todecentration occur. On the other hand, if Px2-1/Py2-1 is not smallerthan the upper limit, i.e. 2.0, the power in the X-direction becomesexcessively large with respect to the power in the Y-direction.Consequently, astigmatic aberrations due to decentration occurundesirably in the opposite direction.

It is even more desirable to satisfy the following condition:0.5<Px2-1/Py2-1<1.5  (4-1)

In the image-forming optical system according to the present invention,focusing of the image-forming optical system can be effected by movingall the constituent elements or moving the prism. However, it is alsopossible to effect focusing by moving the image-formation plane in thedirection of the axial principal ray exiting from the surface (the firstexit surface) closest to the image side. By doing so, it is possible toprevent displacement of the axial principal ray on the entrance side dueto focusing even if the direction in which the axial principal ray fromthe object enters the optical system is not coincident with thedirection of the axial principal ray exiting from the surface closest tothe image side owing to the decentration of the image-forming opticalsystem. It is also possible to effect focusing by moving a plurality ofwedge-shaped prisms, which are formed by dividing a plane-parallelplate, in a direction perpendicular to the Z-axis. In this case also,focusing can be performed independently of the decentration of theimage-forming optical system.

In the present invention, temperature compensation can be made byforming the prism object-side portion and the prism image-side portionusing different materials. By providing these prism portions with powersof different signs, it is possible to prevent the focal shift due tochanges in temperature, which is a problem arising when a plasticmaterial is used to form a prism.

In a case where the two prism portions are cemented together in thepresent invention, it is desirable that each of the two prism portionsshould have a positioning portion for setting a relative position on asurface having no optical action. In a case where two prism portionseach having a reflecting surface with a power are cemented together asin the present invention, in particular, relative displacement of eachprism portion causes the performance to be degraded. Therefore, in thepresent invention, a positioning portion for setting a relative positionis provided on each surface of each prism portion that has no opticalaction, thereby ensuring the required positional accuracy. Thus, thedesired performance can be ensured. In particular, if the two prisms areintegrated into one unit by using the positioning portions and couplingmembers, it becomes unnecessary to perform assembly adjustment.Accordingly, the cost can be further reduced.

Furthermore, the optical path can be folded in a direction differentfrom the decentration direction of the image-forming optical systemaccording to the present invention by placing a reflecting opticalmember, e.g. a mirror, on the object side of the entrance surface of theimage-forming optical system. By doing so, the degree of freedom forlayout of the image-forming optical system further increases, and theoverall size of the image-forming optical apparatus can be furtherreduced.

In the present invention, the image-forming optical system can be formedfrom a prism alone. By doing so, the number of components is reduced,and the cost is lowered. Furthermore, two prisms may be integrated intoone prism with a stop put therebetween. By doing so, the cost can befurther reduced.

In the present invention, the image-forming optical system may includeanother lens (positive or negative lens) as a constituent element inaddition to the prism at either or each of the object and image sides ofthe prism.

The image-forming optical system according to the present invention maybe a fast, single focal length lens system. Alternatively, theimage-forming optical system may be arranged in the form of a zoom lenssystem (variable-magnification image-forming optical system) bycombining it with a single or plurality of refracting optical systemsthat may be provided on the object or image side of the prism or betweentwo prisms.

In the present invention, the refracting and reflecting surfaces of theimage-forming optical system may be formed from spherical surfaces orrotationally symmetric aspherical surfaces, as a matter of course.

In the prism of the present invention, reflecting surfaces other than atotally reflecting surface are preferably formed from a reflectingsurface having a thin film of a metal, e.g. aluminum or silver, formedon the surface thereof, or a reflecting surface formed from a dielectricmultilayer film. In the case of a metal thin film having reflectingaction, a high reflectivity can be readily obtained. The use of adielectric reflecting film is advantageous in a case where a reflectingfilm having wavelength selectivity or minimal absorption is to beformed.

Thus, it is possible to obtain a low-cost and compact image-formingoptical system in which the prism manufacturing accuracy is favorablyeased.

In a case where the above-described image-forming optical systemaccording to the present invention is placed in an image pickup part ofan image pickup apparatus, or in a case where the image pickup apparatusis a photographic apparatus having a camera mechanism, it is possible toadopt an arrangement in which a prism member is placed closest to theobject side among optical elements having an optical action, and theentrance surface of the prism member is decentered with respect to theoptical axis, and further a cover member is placed on the object side ofthe prism member at right angles to the optical axis. The arrangementmay also be such that the prism member has on the object side thereof anentrance surface decentered with respect to the optical axis, and acover lens having a power is placed on the object side of the entrancesurface of the prism member in coaxial relation to the optical axis soas to face the entrance surface across an air spacing.

If the prism member is placed closest to the object side and thedecentered entrance surface is provided on the front side of aphotographic apparatus as stated above, the obliquely tilted entrancesurface is seen from the subject, and it gives the illusion that thephotographic center of the apparatus is deviated from the subject whenthe entrance surface is seen from the subject side. Therefore, a covermember or a cover lens is placed at right angles to the optical axis,thereby preventing the subject from feeling incongruous when seeing theentrance surface, and allowing the subject to be photographed with thesame feeling as in the case of general photographic apparatus.

A finder optical system can be formed by using any of theabove-described image-forming optical systems according to the presentinvention as a finder objective optical system and adding animage-erecting optical system for erecting an object image formed by thefinder objective optical system and an ocular optical system.

In addition, it is possible to construct a camera apparatus by using thefinder optical system and an objective optical system for photographyprovided in parallel to the finder optical system.

In addition, an image pickup optical system can be constructed by usingany of the foregoing image-forming optical systems according to thepresent invention and an image pickup device placed in an image planeformed by the image-forming optical system.

In addition, a camera apparatus can be constructed by using any of theforegoing image-forming optical systems according to the presentinvention as an objective optical system for photography, and a finderoptical system placed in an optical path separate from an optical pathof the objective optical system for photography or in an optical pathsplit from the optical path of the objective optical system forphotography.

In addition, an electronic camera apparatus can be constructed by usingany of the foregoing image-forming optical systems according to thepresent invention, an image pickup device placed in an image planeformed by the image-forming optical system, a recording medium forrecording image information received by the image pickup device, and animage display device that receives image information from the recordingmedium or the image pickup device to form an image for observation.

In addition, an endoscope system can be constructed by using anobservation system having any of the foregoing image-forming opticalsystems according to the present invention and an image transmittingmember for transmitting an image formed by the image-forming opticalsystem along a longitudinal axis, and an illumination system having anilluminating light source and an illuminating light transmitting memberfor transmitting illuminating light from the illuminating light sourcealong the longitudinal axis.

Still other objects and advantages of the invention will in part beobvious and will in part be apparent from the specification.

The invention accordingly comprises the features of construction,combinations of elements, and arrangement of parts which will beexemplified in the construction hereinafter set forth, and the scope ofthe invention will be indicated in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view of an image-forming optical system accordingto Example 1 of the present invention.

FIG. 2 is a sectional view of an image-forming optical system accordingto Example 2 of the present invention.

FIG. 3 is a sectional view of an image-forming optical system accordingto Example 3 of the present invention.

FIG. 4 is a sectional view of an image-forming optical system accordingto Example 4 of the present invention.

FIG. 5 is a sectional view of an image-forming optical system accordingto Example 5 of the present invention.

FIG. 6 is a sectional view of an image-forming optical system accordingto Example 6 of the present invention.

FIG. 7 is a sectional view of an image-forming optical system accordingto Example 7 of the present invention.

FIG. 8 is a sectional view of an image-forming optical system accordingto Example 8 of the present invention.

FIG. 9 is an aberrational diagram showing lateral aberrations in theimage-forming optical system according to Example 1.

FIG. 10 is a perspective view showing the external appearance of anelectronic camera to which an image-forming optical system according tothe present invention is applied, as viewed from the front side thereof.

FIG. 11 is a perspective view of the electronic camera shown in FIG. 10,as viewed from the rear side thereof.

FIG. 12 is a sectional view showing the arrangement of the electroniccamera in FIG. 10.

FIG. 13 is a conceptual view of another electronic camera to which animage-forming optical system according to the present invention isapplied.

FIG. 14 is a conceptual view of a video endoscope system to which animage-forming optical system according to the present invention isapplied.

FIG. 15 is a conceptual view showing an arrangement in which a prismoptical system according to the present invention is applied to aprojection optical system of a presentation system.

FIG. 16 is a diagram showing a desirable arrangement for animage-forming optical system according to the present invention when itis placed in front of an image pickup device.

FIG. 17 is a conceptual view for describing curvature of field producedby a decentered reflecting surface.

FIG. 18 is a conceptual view for describing astigmatism produced by adecentered reflecting surface.

FIG. 19 is a conceptual view for describing coma produced by adecentered reflecting surface.

FIG. 20 is a diagram for describing the definition of the power of adecentered optical system and the power of a decentered optical surface.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Examples 1 to 8 of the image-forming optical system according to thepresent invention will be described below. It should be noted thatconstituent parameters of each example will be shown later.

In Examples 1 to 4, as shown in FIG. 1, an axial principal ray 1 isdefined by a ray emanating from the center of an object and passingthrough the center of a stop 2 to reach the center of an image plane 3.A hypothetic plane is taken in a plane extending through theintersection between the axial principal ray 1 and a first entrancesurface (first surface) 11 of a prism 10 at right angles to the axialprincipal ray 1 incident on the first entrance surface 11. Anotherhypothetic plane is taken in a plane extending through the intersectionbetween the axial principal ray 1 and a first exit surface 16 of theprism 10 at right angles to the axial principal ray 1 exiting from thefirst exit surface 16. The intersection of each hypothetic plane and theassociated optical surface is defined as the origin for decenteredoptical surfaces present between the optical surface and the hypotheticplane subsequent thereto (the image plane in the case of the finalhypothetic plane). In the case of the hypothetic plane determined withrespect to the intersection of the entrance surface, a Z-axis is takenin the direction of the axial principal ray 1 incident thereon. In thecase of the hypothetic plane determined with respect to the intersectionof the exit surface, a Z-axis is taken in the direction of the axialprincipal ray 1 exiting from the exit surface. With respect to the firsthypothetic plane passing through the intersection between the axialprincipal ray 1 and the first entrance surface (first surface) 11 of theprism 10, a positive direction of the Z-axis is taken in the directionof travel of the axial principal ray 1. With respect to the hypotheticplane regarding the first exit surface 16, a positive direction of theZ-axis is taken in the direction of travel of the axial principal ray 1in a case where there are an even number of reflections in the opticalpath from the first hypothetic plane to the hypothetic plane concerned.In a case where the number of reflections is an odd number, a positivedirection of the Z-axis is taken in an opposite direction to thedirection of travel of the axial principal ray 1. A plane containing theZ-axis and the center of the image plane is defined as a YZ-plane. Anaxis extending through the origin at right angles to the YZ-plane isdefined as an X-axis. The direction in which the X-axis extends from theobverse side toward the reverse side of the plane of the figure isdefined as a positive direction of the X-axis. An axis that constitutesa right-handed orthogonal coordinate system in combination with the X-and Z-axes is defined as a Y-axis. FIG. 1 shows the hypothetic planesand a coordinate system concerning the first hypothetic plane determinedwith respect to the intersection of the first entrance surface 11.Illustration of the hypothetic planes and the coordinate system isomitted in FIGS. 2 to 4.

In Examples 5 to 8, as shown in FIG. 5, an axial principal ray 1 isdefined by a ray emanating from the center of an object and passingthrough the center of a stop 2 to reach the center of an image plane 3.A hypothetic plane is taken in a plane extending through theintersection between the axial principal ray 1 and a first entrancesurface (first surface) 11 of a first prism 21 at right angles to theaxial principal ray 1 incident on the first entrance surface 11. Anotherhypothetic plane is taken in a plane extending through the intersectionbetween the axial principal ray 1 and an exit surface 17 of the firstprism 21 at right angles to the axial principal ray 1 exiting from theexit surface 17. Another hypothetic plane is taken in a plane extendingthrough the intersection between the axial principal ray 1 and anentrance surface 18 of a second prism 22 at right angles to the axialprincipal ray 1 incident on the entrance surface 18. Another hypotheticplane is taken in a plane extending through the intersection between theaxial principal ray 1 and a first exit surface 16 of the second prism 22at right angles to the axial principal ray 1 exiting from the first exitsurface 16. The intersection of each hypothetic plane and the associatedoptical surface is defined as the origin for decentered optical surfacespresent between the optical surface and the hypothetic plane subsequentthereto (the image plane in the case of the final hypothetic plane). Inthe case of the hypothetic plane determined with respect to theintersection of each entrance surface, a Z-axis is taken in thedirection of the axial principal ray 1 incident thereon. In the case ofthe hypothetic plane determined with respect to the intersection of eachexit surface, a Z-axis is taken in the direction of the axial principalray 1 exiting from the exit surface. With respect to the firsthypothetic plane passing through the intersection between the axialprincipal ray 1 and the first entrance surface (first surface) 11 of thefirst prism 21, a positive direction of the Z-axis is taken in thedirection of travel of the axial principal ray 1. With respect to theother hypothetic planes, a positive direction of the Z-axis is taken inthe direction of travel of the axial principal ray 1 in a case wherethere are an even number of reflections in the optical path from thefirst hypothetic plane to the hypothetic plane concerned. In a casewhere the number of reflections is an odd number, a positive directionof the Z-axis is taken in an opposite direction to the direction oftravel of the axial principal ray 1. A plane containing the Z-axis andthe center of the image plane is defined as a YZ-plane. An axisextending through the origin at right angles to the YZ-plane is definedas an X-axis. The direction in which the X-axis extends from the obverseside toward the reverse side of the plane of the figure is defined as apositive direction of the X-axis. An axis that constitutes aright-handed orthogonal coordinate system in combination with the X- andZ-axes is defined as a Y-axis. FIG. 5 shows the hypothetic planes and acoordinate system concerning the first hypothetic plane determined withrespect to the intersection of the first entrance surface 11.Illustration of the hypothetic planes and the coordinate system isomitted in FIGS. 6 to 8.

In Examples 1 to 8, the decentration of each surface is made in theYZ-plane, and the one and only plane of symmetry of each rotationallyasymmetric free-form surface is the YZ-plane.

Regarding decentered surfaces, each surface is given displacements inthe X-, Y- and Z-axis directions (X, Y and Z, respectively) of thevertex position of the surface from the origin of the associatedcoordinate system, and tilt angles (degrees) of the center axis of thesurface [the Z-axis of the above equation (a) in regard to free-formsurfaces] with respect to the X-, Y- and Z-axes (α, β and γ,respectively). In this case, the positive α and β mean counterclockwiserotation relative to the positive directions of the corresponding axes,and the positive γ means clockwise rotation relative to the positivedirection of the Z-axis.

Among optical surfaces constituting the optical system in each example,a specific surface (including a hypothetic plane) and a surfacesubsequent thereto are given a surface separation when these surfacesform a coaxial optical system. In addition, the refractive index andAbbe's number of each medium are given according to the conventionalmethod. It should be noted that the sign of the surface separation isshown to be a positive value in a case where there are an even number ofreflections in the optical path from the first hypothetic plane to thereference optical surface (including a hypothetic plane), whereas in acase where the number of reflections is an odd number, the sign of thesurface separation is shown to be a negative value. However, thedistances in the direction of travel of the axial principal ray 1 areall positive values.

The configuration of each free-form surface used in the presentinvention is defined by the above equation (a). The Z-axis of thedefining equation is the axis of the free-form surface.

In the constituent parameters (shown later), those terms concerningfree-form surfaces for which no data is shown are zero. The refractiveindex is expressed by the refractive index for the spectral d-line(wavelength: 587.56 nanometers). Lengths are given in millimeters.

Free-form surfaces may also be defined by Zernike polynomials. That is,the configuration of a free-form surface may be defined by the followingequation (b). The Z-axis of the defining equation (b) is the axis ofZernike polynomial. A rotationally asymmetric surface is defined bypolar coordinates of the height of the Z-axis with respect to theXY-plane. In the equation (b), A is the distance from the Z-axis in theXY-plane, and R is the azimuth angle about the Z-axis, which isexpressed by the angle of rotation measured from the Z-axis.$\begin{matrix}{\begin{matrix}{x = {R \times {\cos(A)}}} \\{y = {R \times {\sin(A)}}}\end{matrix}\quad Z = {D_{2} + {D_{3}R\quad{\cos(A)}} + {D_{4}R\quad{\sin(A)}} + {D_{5}R^{2}\quad{\cos\left( {2A} \right)}} + {D_{6}\left( {R^{2} - 1} \right)} + {D_{7}R^{2}{\sin\left( {2A} \right)}} + {D_{8}R^{3}\quad{\cos\left( {3A} \right)}} + {{D_{9}\left( {{3R^{3}} - {2R}} \right)}\quad{\cos(A)}} + {{D_{10}\left( {{3R^{3}} - {2R}} \right)}{\sin(A)}} + {D_{11}R^{3}{\sin\left( {3A} \right)}} + {D_{12}R^{4}\quad{\cos\left( {4A} \right)}} + {{D_{13}\left( {{4R^{4}} - {3R^{2}}} \right)}\quad{\cos\left( {2A} \right)}} + {D_{14}\left( {{6R^{4}} - {6R^{2}} + 1} \right)} + {{D_{15}\left( {{4R^{4}} - {3R^{2}}} \right)}{\sin\left( {2A} \right)}} + {D_{16}R^{4}{\sin\left( {4A} \right)}} + {D_{17}R^{5}\quad{\cos\left( {5A} \right)}} + {{D_{18}\left( {{5R^{5}} - {4R^{3}}} \right)}\quad{\cos\left( {3A} \right)}} + {{D_{19}\left( {{10R^{5}} - {12R^{3}} + {3R}} \right)}\quad{\cos(A)}} + {{D_{20}\left( {{10R^{5}} - {12R^{3}} + {3R}} \right)}\quad{\sin(A)}} + {{D_{21}\left( {{5R^{5}} - {4R^{3}}} \right)}{\sin\left( {3A} \right)}} + {D_{22}R^{5}{\sin\left( {5A} \right)}} + {D_{23}R^{6}\quad{\cos\left( {6A} \right)}} + {{D_{24}\left( {{6R^{6}} - {5R^{4}}} \right)}\quad{\cos\left( {4A} \right)}} + {{D_{25}\left( {{15R^{6}} - {20R^{4}} + {6R^{2}}} \right)}\quad{\cos\left( {2A} \right)}} + {D_{26}\left( {{20R^{6}} - {30R^{4}} + {12R^{2}} - 1} \right)} + {{D_{27}\left( {{15R^{6}} - {20R^{4}} + {6R^{2}}} \right)}\quad{\sin\left( {2A} \right)}} + {{D_{28}\left( {{6R^{6}} - {5R^{4}}} \right)}{\sin\left( {4A} \right)}} + {D_{29}R^{6}{\sin\left( {6A} \right)}}}} & (b)\end{matrix}$

To design an optical system symmetric with respect to the X-axisdirection, D₄, D₅, D₆, D₁₀, D₁₁, D₁₂, D₁₃, D₁₄, D₂₀, D₂₁, D₂₂ . . .should be used.

Other examples of surfaces usable in the present invention are expressedby the following defining equation (c):Z=ΣΣC _(nm) XY

Assuming that k=7 (polynomial of degree 7), for example, a free-formsurface is expressed by an expanded form of the above equation asfollows: $\begin{matrix}{Z = {C_{2} + {C_{3}y} + {C_{4}{x}} + {C_{5}y^{2}} + {C_{6}y{x}} + {C_{7}x^{2}} + {C_{8}y^{3}} + {C_{9}\quad y^{2}{x}} + {C_{10}y\quad x^{2}} + {C_{11}{x^{3}}} + {C_{12}y^{4}} + {C_{13}y^{3}{x}} + {C_{14}y^{2}x^{2}} + {C_{15}y{x^{3}}} + {C_{16}x^{4}} + {C_{17}y^{5}} + {C_{18}y^{4}{x}} + {C_{19}y^{3}x^{2}} + {C_{20}y^{2}{x^{3}}} + {C_{21}y\quad x^{4}} + {C_{22}{x^{5}}} + {C_{23}y^{6}} + {C_{24}y^{5}{x}} + {C_{25}y^{4}x^{2}} + {C_{26}y^{3}{x^{3}}} + {C_{27}y^{2}x^{4}} + {C_{28}y{x^{5}}} + {C_{29}x^{6}} + {C_{30}y^{7}} + {C_{31}y^{6}{x}} + {C_{32}y^{5}x^{2}} + {C_{33}y^{4}{x^{3}}} + {C_{34}y^{3}x^{4}} + {C_{35}y^{2}{x^{5}}} + {C_{36}y\quad x^{6}} + {C_{35}{x^{7}}}}} & (c)\end{matrix}$

Although in the examples of the present invention the surfaceconfiguration is expressed by a free-form surface using the aboveequation (a), it should be noted that the same advantageous effect canbe obtained by using the above equation (b) or (c).

In all Examples 1 to 8, photographic field angles are as follows: Thehorizontal half field angle is 26.3°, and the vertical half field angleis 20.3°. The image height is 1.6×1.2 millimeters. The entrance pupildiameter is 1.15 millimeters. The focal length is 3.24 millimeters. TheF-number is 2.8. The focal length is equivalent to 35 millimeters interms of the focal length of a silver halide camera. The presentinvention includes not only an image pickup optical system using theimage-forming optical system according to the present invention but alsoan image pickup apparatus incorporating the optical system. Examples 1and 3:

FIGS. 1 and 3 are sectional views of Examples 1 and 3 taken along theYZ-plane containing the axial principal ray. Constituent parameters ofthese examples will be shown later. In the constituent parameters,free-form surfaces are denoted by “FFS”, and hypothetic planes by “HRP”(Hypothetic Reference Plane). The same shall apply to the otherexamples.

Examples 1 and 3 each have, in order in which light passes from theobject side, a stop 2, an object-side portion of a prism 10, animage-side portion of the prism 10, and an image plane (image-formationplane) 3. The object-side portion of the prism 10 comprises a firstentrance surface 11, a first reflecting surface 12, and a secondreflecting surface 13. Light rays are transmitted and reflected by thesesurfaces in the mentioned order. Rays incident on the first reflectingsurface 12 and rays reflected from the second reflecting surface 13intersect each other in the prism 10. An intermediate image plane 4produced by the object-side portion is formed behind the secondreflecting surface 13 (although FIGS. 1 to 8 formally show that theintermediate image plane 4 passes through the intermediate image pointsat right angles to the axial principal ray 1, the intermediate imageplane 4 actually has a rotationally asymmetric curved configurationpassing through the intermediate image points). The intermediate imageplane 4 is formed on the image plane 3 by the image-side portion of theprism 10. The image-side portion of the prism 10 comprises a thirdreflecting surface 14, a fourth reflecting surface 15, and a first exitsurface 16. Light rays are reflected and transmitted by these surfacesin the mentioned order. Rays incident on the third reflecting surface 14and rays reflected from the fourth reflecting surface 15 intersect eachother in the prism 10. In these examples, the direction of rotation of alight beam traveling along a triangular intersecting optical path formedby the first entrance surface 11, the first reflecting surface 12 andthe second reflecting surface 13 is opposite to the direction ofrotation of a light beam traveling along a triangular intersectingoptical path formed by the third reflecting surface 14, the fourthreflecting surface 15 and the first exit surface 16.

In the constituent parameters (shown later), the displacements of eachof the surface Nos. 3 to 9 are expressed by the amounts of displacementfrom the hypothetic plane 1 of surface No. 2. The image plane isexpressed by only the surface separation along the axial principal rayfrom the hypothetic plane 2 of surface No. 9. Examples 2 and 4:

FIGS. 2 and 4 are sectional views of Examples 2 and 4 taken along theYZ-plane containing the axial principal ray. Constituent parameters ofthese examples will be shown later.

Examples 2 and 4 each have, in order in which light passes from theobject side, a stop 2, an object-side portion of a prism 10, animage-side portion of the prism 10, and an image plane (image-formationplane) 3. The object-side portion of the prism 10 comprises a firstentrance surface 11, a first reflecting surface 12, and a secondreflecting surface 13. Light rays are transmitted and reflected by thesesurfaces in the mentioned order. Rays incident on the first reflectingsurface 12 and rays reflected from the second reflecting surface 13intersect each other in the prism 10. An intermediate image plane 4produced by the object-side portion is formed behind the secondreflecting surface 13. The intermediate image plane 4 is formed on theimage plane 3 by the image-side portion of the prism 10. The image-sideportion of the prism 10 comprises a third reflecting surface 14, afourth reflecting surface 15, and a first exit surface 16. Light raysare reflected and transmitted by these surfaces in the mentioned order.Rays incident on the third reflecting surface 14 and rays reflected fromthe fourth reflecting surface 15 intersect each other in the prism 10.In these examples, the direction of rotation of a light beam travelingalong a triangular intersecting optical path formed by the firstentrance surface 11, the first reflecting surface 12 and the secondreflecting surface 13 is the same as the direction of rotation of alight beam traveling along a triangular intersecting optical path formedby the third reflecting surface 14, the fourth reflecting surface 15 andthe first exit surface 16.

In the constituent parameters (shown later), the displacements of eachof the surface Nos. 3 to 9 are expressed by the amounts of displacementfrom the hypothetic plane 1 of surface No. 2. The image plane isexpressed by only the surface separation along the axial principal rayfrom the hypothetic plane 2 of surface No. 9. Examples 5 and 7:

FIGS. 5 and 7 are sectional views of Examples 5 and 7 taken along theYZ-plane containing the axial principal ray. Constituent parameters ofthese examples will be shown later.

Examples 5 and 7 each have, in order in which light passes from theobject side, a stop 2, a first prism 21, a second prism 22, and an imageplane (image-formation plane) 3. The first prism 21 comprises a firstentrance surface 11, a first reflecting surface 12, a second reflectingsurface 13, and a second exit surface 17. Light rays are transmitted,reflected and transmitted by these surfaces in the mentioned order. Raysincident on the first reflecting surface 12 and rays reflected from thesecond reflecting surface 13 intersect each other in the first prism 21.An intermediate image plane 4 produced by the first entrance surface 11,the first reflecting surface 12 and the second reflecting surface 13 isformed between the second reflecting surface 13 and the secondtransmitting surface 17. The intermediate image plane 4 is formed on theimage plane 3 by the second transmitting surface 17 and the second prism22. The second prism 22 comprises a second entrance surface 18, a thirdreflecting surface 14, a fourth reflecting surface 15, and a first exitsurface 16. Light rays are transmitted, reflected and transmitted bythese surfaces in the mentioned order. Rays incident on the thirdreflecting surface 14 and rays reflected from the fourth reflectingsurface 15 intersect each other in the second prism 22. In theseexamples, the direction of rotation of a light beam traveling along atriangular intersecting optical path formed by the first entrancesurface 11, the first reflecting surface 12 and the second reflectingsurface 13 is opposite to the direction of rotation of a light beamtraveling along a triangular intersecting optical path formed by thethird reflecting surface 14, the fourth reflecting surface 15 and thefirst exit surface 16.

In the constituent parameters (shown later), the displacements of eachof the surface Nos. 3 to 7 are expressed by the amounts of displacementfrom the hypothetic plane 1 of surface No. 2. The vertex position of thesurface No. 8 (the hypothetic plane 3) is expressed by only the surfaceseparation along the axial principal ray from the hypothetic plane 2 ofsurface No. 7. The displacements of each of the surface Nos. 9 to 13 areexpressed by the amounts of displacement from the hypothetic plane 3 ofsurface No. 8. The image plane is expressed by only the surfaceseparation along the axial principal ray from the hypothetic plane 4 ofsurface No. 13.

EXAMPLES 6 and 8

FIGS. 6 and 8 are sectional views of Examples 6 and 8 taken along theYZ-plane containing the axial principal ray. Constituent parameters ofthese examples will be shown later.

Examples 6 and 8 each have, in order in which light passes from theobject side, a stop 2, a first prism 21, a second prism 22, and an imageplane (image-formation plane) 3. The first prism 21 comprises a firstentrance surface 11, a first reflecting surface 12, a second reflectingsurface 13, and a second exit surface 17. Light rays are transmitted,reflected and transmitted by these surfaces in the mentioned order. Raysincident on the first reflecting surface 12 and rays reflected from thesecond reflecting surface 13 intersect each other in the first prism 21.An intermediate image plane 4 produced by the first entrance surface 11,the first reflecting surface 12 and the second reflecting surface 13 isformed between the second reflecting surface 13 and the secondtransmitting surface 17. The intermediate image plane 4 is formed on theimage plane 3 by the second transmitting surface 17 and the second prism22. The second prism 22 comprises a second entrance surface 18, a thirdreflecting surface 14, a fourth reflecting surface 15, and a first exitsurface 16. Light rays are transmitted, reflected and transmitted bythese surfaces in the mentioned order. Rays incident on the thirdreflecting surface 14 and rays reflected from the fourth reflectingsurface 15 intersect each other in the second prism 22. In theseexamples, the direction of rotation of a light beam traveling along atriangular intersecting optical path formed by the first entrancesurface 11, the first reflecting surface 12 and the second reflectingsurface 13 is the same as the direction of rotation of a light beamtraveling along a triangular intersecting optical path formed by thethird reflecting surface 14, the fourth reflecting surface 15 and thefirst exit surface 16.

In the constituent parameters (shown later), the displacements of eachof the surface Nos. 3 to 7 are expressed by the amounts of displacementfrom the hypothetic plane 1 of surface No. 2. The vertex position of thesurface No. 8 (the hypothetic plane 3) is expressed by only the surfaceseparation along the axial principal ray from the hypothetic plane 2 ofsurface No. 7. The displacements of each of the surface Nos. 9 to 13 areexpressed by the amounts of displacement from the hypothetic plane 3 ofsurface No. 8. The image plane is expressed by only the surfaceseparation along the axial principal ray from the hypothetic plane 4 ofsurface No. 13.

Constituent parameters in the foregoing Examples 1 to 8 are shown below.In the tables below, “FFS” denotes a free-form surface, and “HRP”denotes a hypothetic plane.

EXAMPLE 1

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ −1000.00 plane 1 ∞ (Stop)    0.10 2 ∞ (H R P 1) 3 F F S {circle around (1)} (1) 1.4924 57.6 4 F FS {circle around (2)} (2) 1.4924 57.6 5 F F S {circle around (3)} (3)1.4924 57.6 6 F F S {circle around (4)} (4) 1.4924 57.6 7 F F S {circlearound (5)} (5) 1.4924 57.6 8 F F S {circle around (6)} (6) 9 ∞ (H R P2)     2.60 (7) Image ∞ plane F F S {circle around (1)} C₄ 1.4745 × 10⁻¹C₆ 7.9582 × 10⁻² F F S {circle around (2)} C₄ −3.9949 × 10⁻²   C₆−1.8820 × 10⁻²   F F S {circle around (3)} C₄ 3.7493 × 10⁻² C₆ 3.8549 ×10⁻² F F S {circle around (4)} C₄ −7.7376 × 10⁻³   C₆ −7.8124 × 10⁻³   FF S {circle around (5)} C₄ 3.9556 × 10⁻² C₆ 3.7486 × 10⁻² F F S {circlearound (6)} C₄ 1.8864 × 10⁻³ C₆ 1.4064 × 10⁻² Displacement and tilt (1)X 0.00 Y 0.00 Z 0.00 α 13.83 β 0.00 γ 0.00 Displacement and tilt (2) X0.00 Y −1.06 Z 6.53 α 13.29 β 0.00 γ 0.00 Displacement and tilt (3) X0.00 Y −3.99 Z 2.47 α 58.29 β 0.00 γ 0.00 Displacement and tilt (4) X0.00 Y 0.00 Z 9.94 α −22.50 β 0.00 γ 0.00 Displacement and tilt (5) X0.00 Y 3.16 Z 6.79 α −67.50 β 0.00 γ 0.00 Displacement and tilt (6) X0.00 Y −1.73 Z 6.79 α −105.63 β 0.00 γ 0.00 Displacement and tilt (7) X0.00 Y −1.73 Z 6.79 α −81.92 β 0.00 γ 0.00

EXAMPLE 2

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ −1000.00 plane 1 ∞ (Stop)    0.10 2 ∞ (H R P 1) 3 F F S {circle around (1)} (1) 1.4924 57.6 4 F FS {circle around (2)} (2) 1.4924 57.6 5 F F S {circle around (3)} (3)1.4924 57.6 6 F F S {circle around (4)} (4) 1.4924 57.6 7 F F S {circlearound (5)} (5) 1.4924 57.6 8 F F S {circle around (6)} (6) 9 ∞ (H R P2)     3.48 (7) Image ∞ plane F F S {circle around (1)} C₄ 1.1940 × 10⁻²C₆ −1.0089 × 10⁻²   F F S {circle around (2)} C₄ −3.9281 × 10⁻²   C₆−3.8396 × 10⁻²   F F S {circle around (3)} C₄ 2.2247 × 10⁻² C₆ 2.7872 ×10⁻² F F S {circle around (4)} C₄ −2.7563 × 10⁻²   C₆ −3.4063 × 10⁻²   FF S {circle around (5)} C₄ 2.2540 × 10⁻² C₆ 2.6264 × 10⁻³ F F S {circlearound (6)} C₄ −4.4925 × 10⁻²   C₆ −3.3645 × 10⁻²   Displacement andtilt (1) X 0.00 Y 0.00 Z 0.00 α −31.21 β 0.00 γ 0.00 Displacement andtilt (2) X 0.00 Y 1.69 Z 4.55 α 42.82 β 0.00 γ 0.00 Displacement andtilt (3) X 0.00 Y −1.46 Z 3.11 α 87.82 β 0.00 γ 0.00 Displacement andtilt (4) X 0.00 Y 0.00 Z 10.15 α 22.50 β 0.00 γ 0.00 Displacement andtilt (5) X 0.00 Y −3.49 Z 6.66 α 67.50 β 0.00 γ 0.00 Displacement andtilt (6) X 0.00 Y 2.18 Z 6.66 α 110.74 β 0.00 γ 0.00 Displacement andtilt (7) X 0.00 Y 2.18 Z 6.66 α 78.84 β 0.00 γ 0.00

EXAMPLE 3

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ −1000.00 plane 1 ∞ (Stop)    0.10 2 ∞ (H R P 1) 3 F F S {circle around (1)} (1) 1.4924 57.6 4 F FS {circle around (2)} (2) 1.4924 57.6 5 F F S {circle around (3)} (3)1.4924 57.6 6 F F S {circle around (4)} (4) 1.4924 57.6 7 F F S {circlearound (5)} (5) 1.4924 57.6 8 F F S {circle around (6)} (6) 9 ∞ (H R P2)     2.03 (7) Image ∞ plane F F S {circle around (1)} C₄   8.5814 ×10⁻² C₆   9.7753 × 10⁻³ C₈ 4.9999 × 10⁻³ C₁₃ −5.7617 × 10⁻⁴ F F S{circle around (2)} C₄ −4.0084 × 10⁻² C₆ −1.4944 × 10⁻² C₈ 1.9913 × 10⁻³C₁₀ −7.0248 × 10⁻⁶ C₁₁   6.2670 × 10⁻⁴ C₁₃ −1.9283 × 10⁻⁴   C₁₅ −9.5320× 10⁻⁵ F F S {circle around (3)} C₄   1.0574 × 10⁻² C₆    3.7396 × 10⁻²C₈ 6.2001 × 10⁻³ C₁₀    6.0873 × 10⁻⁴ C₁₁    4.6910 × 10⁻⁴ C₁₃ −9.8193 ×10⁻⁴   C₁₅ −2.9008 × 10⁻⁴ F F S {circle around (4)} C₄ −2.8107 × 10⁻² C₆−2.1096 × 10⁻² C₈ 3.3309 × 10⁻⁴ C₁₀    1.2654 × 10⁻³ C₁₁    1.3182 ×10⁻⁴ C₁₃ 5.2249 × 10⁻⁴ C₁₅    1.8213 × 10⁻⁴ F F S {circle around (5)} C₄   2.8668 × 10⁻² C₆    3.3258 × 10⁻² C₈ −6.3656 × 10⁻⁴   C₁₀ −4.3304 ×10⁻⁴ C₁₁    1.7981 × 10⁻⁵ C₁₃ 4.1170 × 10⁻⁴ C₁₅    1.1474 × 10⁻⁴ F F S{circle around (6)} C₄    4.5920 × 10⁻³ C₆    3.4434 × 10⁻³ C₈ −2.4885 ×10⁻²   C₁₃    7.8349 × 10⁻³ Displacement and tilt (1) X 0.00 Y 0.00 Z0.00 α 2.31 β 0.00 γ 0.00 Displacement and tilt (2) X 0.00 Y −0.17 Z6.18 α 25.20 β 0.00 γ 0.00 Displacement and tilt (3) X 0.00 Y −3.90 Z3.25 α 70.97 β 0.00 γ 0.00 Displacement and tilt (4) X 0.00 Y 0.00 Z8.46 α −19.10 β 0.00 γ 0.00 Displacement and tilt (5) X 0.00 Y 2.63 Z5.11 α −68.53 β 0.00 γ 0.00 Displacement and tilt (6) X 0.00 Y −2.08 Z4.38 α −100.20 β 0.00 γ 0.00 Displacement and tilt (7) X 0.00 Y −2.08 Z4.38 α −98.20 β 0.00 γ 0.00

EXAMPLE 4

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ −1000.00 plane 1 ∞ (Stop)    0.10 2 ∞ (H R P 1) 3 F F S {circle around (1)} (1) 1.4924 57.6 4 F FS {circle around (2)} (2) 1.4924 57.6 5 F F S {circle around (3)} (3)1.4924 57.6 6 F F S {circle around (4)} (4) 1.4924 57.6 7 F F S {circlearound (5)} (5) 1.4924 57.6 8 F F S {circle around (6)} (6) 9 ∞ (H R P2)     2.84 (7) Image ∞ plane F F S {circle around (1)} C₄   5.0413 ×10⁻² C₆ −3.7336 × 10⁻² C₈   4.9418 × 10⁻² C₁₀ −1.4142 × 10⁻² C₁₁   1.3334 × 10⁻² C₁₃    2.3396 × 10⁻² C₁₅ −1.8589 × 10⁻⁴ F F S {circlearound (2)} C₄ −4.0862 × 10⁻² C₆ −3.8025 × 10⁻² C₈   1.5530 × 10⁻⁴ C₁₀−1.3834 × 10⁻³ C₁₁    3.2358 × 10⁻⁴ C₁₃ −2.4997 × 10⁻⁴ C₁₅ −1.5955 ×10⁻⁴ F F S {circle around (3)} C₄    1.2784 × 10⁻² C₆    3.6059 × 10⁻²C₈    7.7983 × 10⁻³ C₁₀    2.9294 × 10⁻³ F F S {circle around (4)} C₄−1.6942 × 10⁻² C₆ −2.7882 × 10⁻² C₈ −1.8823 × 10⁻³ C₁₀   4.5839 × 10⁻⁴C₁₁    1.7036 × 10⁻⁴ C₁₃    5.5053 × 10⁻⁵ C₁₅    4.1621 × 10⁻⁵ F F S{circle around (5)} C₄   3.7553 × 10⁻² C₆    2.0240 × 10⁻² C₈ −9.7555 ×10⁻⁴ C₁₀    1.7498 × 10⁻³ C₁₁    5.4919 × 10⁻⁵ C₁₃ −4.5536 × 10⁻⁵ C₁₅  1.2522 × 10⁻⁴ F F S {circle around (6)} C₄   8.8112 × 10⁻² C₆   1.2154 × 10⁻¹ C₈ −7.5941 × 10⁻² C₁₀ −5.8052 × 10⁻³ C₁₁    9.6458 × 10⁻³C₁₃ −2.7619 × 10⁻³ C₁₅    1.4379 × 10⁻² Displacement and tilt (1) X 0.00Y 0.00 Z 0.00 α −15.02 β 0.00 γ 0.00 Displacement and tilt (2) X 0.00 Y0.89 Z 5.03 α 32.50 β 0.00 γ 0.00 Displacement and tilt (3) X 0.00 Y−2.26 Z 2.83 α 77.50 β 0.00 γ 0.00 Displacement and tilt (4) X 0.00 Y0.00 Z 10.89 α 22.50 β 0.00 γ 0.00 Displacement and tilt (5) X 0.00 Y−3.21 Z 7.68 α 67.50 β 0.00 γ 0.00 Displacement and tilt (6) X 0.00 Y1.90 Z 7.68 α 102.09 β 0.00 γ 0.00 Displacement and tilt (7) X 0.00 Y1.90 Z 7.68 α 83.87 β 0.00 γ 0.00

EXAMPLE 5

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ −1000.00 plane 1 ∞ (Stop)    0.10 2 ∞ (H R P 1) 3 F F S {circle around (1)} (1) 1.4924 57.6 4 F FS {circle around (2)} (2) 1.4924 57.6 5 F F S {circle around (3)} (3)1.4924 57.6 6 F F S {circle around (4)} (4) 7 ∞ (H R P 2)      1.07 (5)8 ∞ (H R P 3) 9 F F S {circle around (5)} (6) 1.4924 57.6 10 F F S{circle around (6)} (7) 1.4924 57.6 11 F F S {circle around (7)} (8)1.4924 57.6 12 F F S {circle around (8)} (9) 13 ∞ (H R P 4)      2.07(10) Image ∞ plane F F S {circle around (1)} C₄   9.9415 × 10⁻² C₆−1.0251 × 10⁻² F F S {circle around (2)} C₄ −3.1777 × 10⁻² C₆ −4.1381 ×10⁻² F F S {circle around (3)} C₄   1.0921 × 10⁻² C₆   1.9864 × 10⁻³ F FS {circle around (4)} C₄ −1.3947 × 10⁻¹ C₆ −8.2631 × 10⁻² F F S {circlearound (5)} C₄ −1.7628 × 10⁻² C₆   8.3247 × 10⁻² F F S {circle around(6)} C₄ −1.3188 × 10⁻² C₆ −2.2426 × 10⁻² F F S {circle around (7)} C₄  3.3408 × 10⁻² C₆   1.6172 × 10⁻² F F S {circle around (8)} C₄ −2.0179× 10⁻² C₆ −7.7184 × 10⁻² Displacement and tilt (1) X 0.00 Y 0.00 Z 0.00α 0.45 β 0.00 γ 0.00 Displacement and tilt (2) X 0.00 Y −0.03 Z 5.39 α19.49 β 0.00 γ 0.00 Displacement and tilt (3) X 0.00 Y −2.43 Z 2.46 α63.66 β 0.00 γ 0.00 Displacement and tilt (4) X 0.00 Y 2.62 Z 2.63 α93.65 β 0.00 γ 0.00 Displacement and tilt (5) X 0.00 Y 2.62 Z 2.63 α85.26 β 0.00 γ 0.00 Displacement and tilt (6) X 0.00 Y 0.00 Z 0.00 α−0.10 β 0.00 γ 0.00 Displacement and tilt (7) X 0.00 Y 0.00 Z 7.03 α−26.24 β 0.00 γ 0.00 Displacement and tilt (8) X 0.00 Y 3.27 Z 4.52 α−71.85 β 0.00 γ 0.00 Displacement and tilt (9) X 0.00 Y −2.68 Z 4.39 α−97.19 β 0.00 γ 0.00 Displacement and tilt (10) X 0.00 Y −2.68 Z 4.39 α−88.32 β 0.00 γ 0.00

EXAMPLE 6

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ −1000.00 plane 1 ∞ (Stop)    0.10 2 ∞ (H R P 1) 3 F F S {circle around (1)} (1) 1.4924 57.6 4 F FS {circle around (2)} (2) 1.4924 57.6 5 F F S {circle around (3)} (3)1.4924 57.6 6 F F S {circle around (4)} (4) 7 ∞ (H R P 2)     0.97 (5) 8∞ (H R P 3) 9 F F S {circle around (5)} (6) 1.4924 57.6 10 F F S {circlearound (6)} (7) 1.4924 57.6 11 F F S {circle around (7)} (8) 1.4924 57.612 F F S {circle around (8)} (9) 13 ∞ (H R P 4)     2.40 (10) Image ∞plane F F S {circle around (1)} C₄   1.1706 × 10⁻¹ C₆ −5.6558 × 10⁻² F FS {circle around (2)} C₄ −2.0385 × 10⁻² C₆ −3.1632 × 10⁻² F F S {circlearound (3)} C₄   1.2591 × 10⁻² C₆   2.8642 × 10⁻² F F S {circle around(4)} C₄ −1.3808 × 10⁻¹ C₆ −9.3678 × 10⁻² F F S {circle around (5)} C₄−4.4289 × 10⁻² C₆   3.3935 × 10⁻² F F S {circle around (6)} C₄ −2.1843 ×10⁻² C₆ −3.2128 × 10⁻² F F S {circle around (7)} C₄   2.0501 × 10⁻² C₆   3.0838 × 10⁻³ F F S {circle around (8)} C₄ −1.1510 × 10⁻¹ C₆ −1.6756× 10⁻³ Displacement and tilt (1) X 0.00 Y 0.00 Z 0.00 α −13.86 β 0.00 γ0.00 Displacement and tilt (2) X 0.00 Y 0.78 Z 4.77 α 35.40 β 0.00 γ0.00 Displacement and tilt (3) X 0.00 Y −2.16 Z 3.18 α 82.52 β 0.00 γ0.00 Displacement and tilt (4) X 0.00 Y 4.33 Z 1.62 α 104.75 β 0.00 γ0.00 Displacement and tilt (5) X 0.00 Y 4.33 Z 1.62 α 102.85 β 0.00 γ0.00 Displacement and tilt (6) X 0.00 Y 0.00 Z 0.00 α 0.80 β 0.00 γ 0.00Displacement and tilt (7) X 0.00 Y 0.03 Z 7.09 α 25.76 β 0.00 γ 0.00Displacement and tilt (8) X 0.00 Y −2.36 Z 5.16 α 78.05 β 0.00 γ 0.00Displacement and tilt (9) X 0.00 Y 3.60 Z 3.58 α 117.95 β 0.00 γ 0.00Displacement and tilt (10) X 0.00 Y 3.60 Z 3.58 α 98.20 β 0.00 γ 0.00

EXAMPLE 7

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ −1000.00 plane 1 ∞ (Stop)    0.11 2 ∞ (H R P 1) 3 F F S {circle around (1)} (1) 1.4924 57.6 4 F FS {circle around (2)} (2) 1.4924 57.6 5 F F S {circle around (3)} (3)1.4924 57.6 6 F F S {circle around (4)} (4) 7 ∞ (H R P 2)     1.31 (5) 8∞ (H R P 3) 9 F F S {circle around (5)} (6) 1.4924 57.6 10 F F S {circlearound (6)} (7) 1.4924 57.6 11 F F S {circle around (7)} (8) 1.4924 57.612 F F S {circle around (8)} (9) 13 ∞ (H R P 4)     2.11 (10) Image ∞plane F F S {circle around (1)} C₄   7.9718 × 10⁻² C₆ −1.1269 × 10⁻² C₈−1.0176 × 10⁻² C₁₀ −2.6805 × 10⁻² C₁₁    1.6790 × 10⁻³ C₁₃    1.5078 ×10⁻³ C₁₅ −6.3750 × 10⁻³ F F S {circle around (2)} C₄ −4.6138 × 10⁻² C₆−4.8462 × 10⁻² C₈ −4.4935 × 10⁻⁵ C₁₀ −7.7648 × 10⁻⁴ C₁₁    5.4654 × 10⁻⁴C₁₃ −2.2718 × 10⁻⁴ C₁₅ −1.4747 × 10⁻⁴ F F S {circle around (3)} C₄  1.3369 × 10⁻² C₆   9.0659 × 10⁻³ C₈   9.7824 × 10⁻³ C₁₀ −1.7847 × 10⁻³C₁₁ −1.0220 × 10⁻³ C₁₃ −2.0190 × 10⁻³ C₁₅ −1.2885 × 10⁻³ F F S {circlearound (4)} C₄ −1.5289 × 10⁻¹ C₆ −1.4219 × 10⁻¹ C₈   5.0554 × 10⁻³ C₁₀−8.5660 × 10⁻³ C₁₁ −1.4963 × 10⁻³ C₁₃    8.8480 × 10⁻⁴ C₁₅ −7.7840 ×10⁻⁴ F F S {circle around (5)} C₄ −8.6606 × 10⁻² C₆ −3.9618 × 10⁻² C₈−5.2433 × 10⁻³ C₁₀ −2.0308 × 10⁻² C₁₁ −1.6410 × 10⁻⁴ C₁₃   7.6935 × 10⁻⁴C₁₅ −5.7553 × 10⁻⁴ F F S {circle around (6)} C₄ −1.8763 × 10⁻² C₆−2.2577 × 10⁻² C₈ −5.4033 × 10⁻⁴ C₁₀ −3.6774 × 10⁻⁴ C₁₁    5.2947 × 10⁻⁵C₁₃ −5.7964 × 10⁻⁵ C₁₅ −7.9440 × 10⁻⁶ F F S {circle around (7)} C₄  3.1927 × 10⁻² C₆    1.6149 × 10⁻² C₈ −1.5527 × 10⁻³ C₁₀ −9.9188 × 10⁻⁴C₁₁    6.7759 × 10⁻⁶ C₁₃ −8.4522 × 10⁻⁵ C₁₅    1.1927 × 10⁻⁵ F F S{circle around (8)} C₄    8.2308 × 10⁻² C₆   4.6678 × 10⁻² C₈ −2.7504 ×10⁻² C₁₀    4.9285 × 10⁻³ C₁₁    3.1889 × 10⁻⁴ C₁₃    1.4557 × 10⁻³ C₁₅   6.0455 × 10⁻³ Displacement and tilt (1) X 0.00 Y 0.00 Z 0.00 α −0.81β 0.00 γ 0.00 Displacement and tilt (2) X 0.00 Y 0.05 Z 5.52 α 19.05 β0.00 γ 0.00 Displacement and tilt (3) X 0.00 Y −2.55 Z 2.14 α 62.09 β0.00 γ 0.00 Displacement and tilt (4) X 0.00 Y 2.65 Z 2.45 α 96.69 β0.00 γ 0.00 Displacement and tilt (5) X 0.00 Y 2.65 Z 2.45 α 81.57 β0.00 γ 0.00 Displacement and tilt (6) X 0.00 Y 0.00 Z 0.00 α 13.38 β0.00 γ 0.00 Displacement and tilt (7) X 0.00 Y 0.55 Z 7.02 α −25.04 β0.00 γ 0.00 Displacement and tilt (8) X 0.00 Y 3.04 Z 5.24 α −79.35 β0.00 γ 0.00 Displacement and tilt (9) X 0.00 Y −2.83 Z 3.76 α −102.06 β0.00 γ 0.00 Displacement and tilt (10) X 0.00 Y −2.83 Z 3.76 α −105.20 β0.00 γ 0.00

EXAMPLE 8

Surface Radius of Surface Displacement Refractive Abbe's No. curvatureseparation and tilt index No. Object ∞ −1000.00 plane 1 ∞ (Stop)    0.10 2 ∞ (H R P 1) 3 F F S {circle around (1)} (1) 1.4924 57.6 4 F FS {circle around (2)} (2) 1.4924 57.6 5 F F S {circle around (3)} (3)1.4924 57.6 6 F F S {circle around (4)} (4) 7 ∞ (H R P 2)     1.08 (5) 8∞ (H R P 3) 9 F F S {circle around (5)} (6) 1.4924 57.6 10 F F S {circlearound (6)} (7) 1.4924 57.6 11 F F S {circle around (7)} (8) 1.4924 57.612 F F S {circle around (8)} (9) 13 ∞ (H R P 4)     2.05 (10) Image ∞plane F F S {circle around (1)} C₄    4.6940 × 10⁻² C₆ −5.4801 × 10⁻² C₈  2.4076 × 10⁻² C₁₀ −2.5017 × 10⁻² C₁₁    7.6467 × 10⁻³ C₁₃    2.4375 ×10⁻² C₁₅ −2.6368 × 10⁻³ F F S {circle around (2)} C₄ −3.8851 × 10⁻² C₆−4.5014 × 10⁻² C₈ −2.0800 × 10⁻⁴ C₁₀ −1.3013 × 10⁻³ C₁₁ −5.5109 × 10⁻⁵C₁₃ −4.1175 × 10⁻⁵ C₁₅ −4.3413 × 10⁻⁵ F F S {circle around (3)} C₄  1.5483 × 10⁻² C₆    5.8148 × 10⁻³ C₈   7.2040 × 10⁻³ C₁₀ −1.0978 ×10⁻³ C₁₁ −2.5074 × 10⁻⁴ C₁₃   7.1064 × 10⁻⁴ C₁₅ −4.0019 × 10⁻⁴ F F S{circle around (4)} C₄ −4.2258 × 10⁻² C₆ −1.6036 × 10⁻¹ C₈ −4.3143 ×10⁻² C₁₀ −2.0643 × 10⁻⁴ C₁₁   2.9217 × 10⁻³ C₁₃    2.9462 × 10⁻³ C₁₅−7.6527 × 10⁻⁴ F F S {circle around (5)} C₄ −4.9187 × 10⁻² C₆ −8.3739 ×10⁻² C₈ −4.6136 × 10⁻² C₁₀ −2.3379 × 10⁻² C₁₁    1.6330 × 10⁻⁴ C₁₃−3.2823 × 10⁻³ C₁₅    1.2878 × 10⁻³ F F S {circle around (6)} C₄ −2.7971× 10⁻² C₆ −2.9992 × 10⁻² C₈ −1.1174 × 10⁻³ C₁₀ −1.3738 × 10⁻⁵ C₁₁   9.6373 × 10⁻⁵ C₁₃    3.9779 × 10⁻⁵ C₁₅    3.1647 × 10⁻⁵ F F S {circlearound (7)} C₄   2.8295 × 10⁻² C₆   9.2540 × 10⁻³ C₈   9.1533 × 10⁻⁴ C₁₀   1.2919 × 10⁻³ C₁₁    6.1071 × 10⁻⁵ C₁₃ −5.1722 × 10⁻⁵ C₁₅    1.6654 ×10⁻⁴ F F S {circle around (8)} C₄   1.2536 × 10⁻¹ C₆   6.8961 × 10⁻³ C₈−7.0960 × 10⁻² C₁₀ −8.5531 × 10⁻³ C₁₁    2.4529 × 10⁻² C₁₃ −9.8519 ×10⁻³ C₁₅   3.0143 × 10⁻⁴ Displacement and tilt (1) X 0.00 Y 0.00 Z 0.00α −11.36 β 0.00 γ 0.00 Displacement and tilt (2) X 0.00 Y 0.74 Z 5.54 α30.35 β 0.00 γ 0.00 Displacement and tilt (3) X 0.00 Y −1.96 Z 3.51 α79.66 β 0.00 γ 0.00 Displacement and tilt (4) X 0.00 Y 4.73 Z 1.56 α117.16 β 0.00 γ 0.00 Displacement and tilt (5) X 0.00 Y 4.73 Z 1.56 α100.69 β 0.00 γ 0.00 Displacement and tilt (6) X 0.00 Y 0.00 Z 0.00 α4.88 β 0.00 γ 0.00 Displacement and tilt (7) X 0.00 Y 0.18 Z 6.51 α29.22 β 0.00 γ 0.00 Displacement and tilt (8) X 0.00 Y −2.40 Z 4.82 α84.33 β 0.00 γ 0.00 Displacement and tilt (9) X 0.00 Y 2.98 Z 2.66 α113.54 β 0.00 γ 0.00 Displacement and tilt (10) X 0.00 Y 2.98 Z 2.66 α111.00 β 0.00 γ 0.00

FIG. 9 is an aberrational diagram showing lateral aberrations in theabove-described Example 1. In the diagram showing lateral aberrations,the numerals in the parentheses denote (horizontal (X-direction) fieldangle, vertical (Y-direction) field angle), and lateral aberrations atthe field angles are shown.

It should be noted that the values of the conditions (1) to (4) in theabove-described Examples 1 to 8 are as follows:

Examples Conditions 1 2 3 4 5 6 7 8 (1) 0.86 0.87 0.77 0.80 0.71 0.470.90 0.77 (2) 0.80 0.49 0.20 0.25 0.24 0.29 0.26 0.30 (3) 0.17 0.61 0.540.33 0.30 0.50 0.37 0.55 (4) 0.99 0.81 1.33 0.61 0.59 0.68 0.83 0.93

Incidentally, the above-described image-forming optical system accordingto the present invention can be used in photographic apparatus,particularly in cameras, in which an object image formed by theimage-forming optical system is received with an image pickup device,such as a CCD or a silver halide film, to take a photograph of theobject. It is also possible to use the image-forming optical system asan objective optical system of an observation apparatus in which anobject image is viewed through an ocular lens, particularly a finderunit of a camera. The image-forming optical system according to thepresent invention is also usable as an image pickup optical system foroptical apparatus using a small-sized image pickup device, e.g.endoscopes. Embodiments in which the present invention is applied tosuch apparatuses will be described below.

FIGS. 10 to 12 are conceptual views showing an arrangement in which theimage-forming optical system according to the present invention isincorporated into an objective optical system in a finder unit of anelectronic camera. FIG. 10 is a perspective view showing the externalappearance of an electronic camera 40 as viewed from the front sidethereof. FIG. 11 is a perspective view of the electronic camera 40 asviewed from the rear side thereof. FIG. 12 is a sectional view showingthe arrangement of the electronic camera 40. In the illustrated example,the electronic camera 40 includes a photographic optical system 41having an optical path 42 for photography, a finder optical system 43having an optical path 44 for the finder, a shutter 45, a flash 46, aliquid crystal display monitor 47, etc. When the shutter 45, which isplaced on the top of the camera 40, is depressed, photography isperformed through an objective optical system 48 for photography. Anobject image produced by the objective optical system 48 for photographyis formed on an image pickup surface 50 of a CCD 49 through a filter 51,e.g. a low-pass filter, an infrared cutoff filter, etc. The object imagereceived by the CCD 49 is processed in a processor 52 and displayed asan electronic image on the liquid crystal display monitor 47, which isprovided on the rear of the camera 40. The processor 52 is provided witha memory or the like to enable the photographed electronic image to berecorded. It should be noted that the memory may be provided separatelyfrom the processor 52. The arrangement may also be such that thephotographed electronic image is electronically recorded or written on afloppy disk or the like. The camera 40 may be arranged in the form of asilver halide camera in which a silver halide film is disposed in placeof the CCD 49.

Furthermore, an objective optical system 53 for the finder is placed inthe optical path 44 for the finder. The objective optical system 53 forthe finder comprises a cover lens 54, a stop 2, a prism 10 and afocusing lens 66. The stop 2 and the prism 10 constitute animage-forming optical system. An optical system of the same type asExample 1 is used as the image-forming optical system. The cover lens 54used as a cover member is a lens having a negative power to enlarge thefield angle. The focusing lens 66, which is placed behind the prism 10,can be moved in the forward and backward directions along the opticalaxis to adjust the position thereof. The focusing lens 66 is used forfocusing the objective optical system 53 for the finder. An object imageproduced on an image-formation plane 67 by the objective optical system53 for the finder is formed on a view frame 57 of a Porro prism 55,which is an image-erecting member. It should be noted that the viewframe 57 is placed between a first reflecting surface 56 and secondreflecting surface 58 of the Porro prism 55. An ocular optical system 59is placed behind the Porro prism 55 to lead an erect image to anobserver's eyeball E.

In the camera 40, which is arranged as stated above, the objectiveoptical system 53 for the finder can be constructed with a minimalnumber of optical members. Accordingly, a high-performance and low-costcamera can be realized. In addition, because the optical path of theobjective optical system 53 can be folded, the degree of freedom withwhich the constituent elements can be arranged in the camera increases.This is favorable for design.

Although no mention is made of the arrangement of the objective opticalsystem 48 for photography in the electronic camera 40 shown in FIG. 12,it should be noted that the objective optical system 48 for photographymay be formed by using not only a refracting coaxial optical system butalso any type of image-forming optical systems according to the presentinvention, which comprise a single prism 10 or two prisms 21 and 22.

FIG. 13 is a conceptual view showing an arrangement in which animage-forming optical system according to the present invention isincorporated into an objective optical system 48 in a photography partof an electronic camera 40. In this example, an image-forming opticalsystem similar to Example 5 is used in the objective optical system 48for photography, which is placed in an optical path 42 for photography.An object image produced by the objective optical system for photographyis formed on an image pickup surface 50 of a CCD 49 through a filter 51,e.g. a low-pass filter, an infrared cutoff filter, etc. The object imagereceived by the CCD 49 is processed in a processor 52 and displayed inthe form of an electronic image on a liquid crystal display device (LCD)60. The processor 52 also controls a recording device 61 for recordingthe object image detected by the CCD 49 in the form of electronicinformation. The image displayed on the LCD 60 is led to an observer'seyeball E through an ocular optical system 59. The ocular optical system59 is formed from a decentered prism. In this example, the ocularoptical system 59 has three surfaces, i.e. an entrance surface 62, areflecting surface 63, and a surface 64 serving as both reflecting andrefracting surfaces. At least one of the two surfaces 63 and 64 having areflecting action, preferably each of them, is formed from aplane-symmetry free-form surface with only one plane of symmetry thatgives a power to a light beam and corrects decentration aberrations. Theonly one plane of symmetry is formed in approximately the same plane asthe only one plane of symmetry of the plane-symmetry free-form surfacesof the prisms 21 and 22 in the objective optical system 48 forphotography. The objective optical system 48 for photography may includeanother lens (positive or negative lens) as a constituent element on theobject or image side of the prisms 21 and 22 or therebetween.

In the camera 40 arranged as stated above, the objective optical system48 for photography can be constructed with a minimal number of opticalmembers. Accordingly, a high-performance and low-cost camera can berealized. In addition, because all the constituent elements of theoptical system can be arranged in the same plane, it is possible toreduce the thickness in a direction perpendicular to the plane in whichthe constituent elements are arranged.

Although in this example a plane-parallel plate is placed as a covermember 65 of the objective optical system 48 for photography, it is alsopossible to use a lens having a power as the cover member 65 as in thecase of the above-described example.

The surface closest to the object side in the image-forming opticalsystem according to the present invention may be used as a cover memberinstead of providing a cover member separately. In this example, theentrance surface of the prism 10 is the closest to the object side inthe image-forming optical system. In such a case, however, because theentrance surface is decentered with respect to the optical axis, if thissurface is placed on the front side of the camera, it gives the illusionthat the photographic center of the camera 40 is deviated from thesubject when the entrance surface is seen from the subject side (thesubject normally feels that photographing is being performed in adirection perpendicular to the entrance surface, as in the case ofordinary cameras). Thus, the entrance surface would give a sense ofincongruity. Therefore, in a case where the surface of the image-formingoptical system that is closest to the object side is a decenteredsurface as in this example, it is desirable to provide the cover member65 (or cover lens 54) from the viewpoint of preventing the subject fromfeeling incongruous when seeing the entrance surface, and allowing thesubject to be photographed with the same feeling as in the case of theexisting cameras.

FIG. 14 is a conceptual view showing an arrangement in which theimage-forming optical system according to the present invention isincorporated into an objective optical system 82 in an observationsystem of a video endoscope system, and the image-forming optical systemaccording to the present invention is also incorporated into an ocularoptical system 87 in the observation system of the video endoscopesystem. In this example, the objective optical system 82 in theobservation system uses an optical system similar to Example 1, and theocular optical system 87 uses an optical system similar to Example 5. Asshown in part (a) of FIG. 14, the video endoscope system includes avideo endoscope 71, a light source unit 72 for supplying illuminatinglight, a video processor 73 for executing processing of signalsassociated with the video endoscope 71, a monitor 74 for displayingvideo signals output from the video processor 73, a VTR deck 75 and avideo disk 76, which are connected to the video processor 73 to recordvideo signals and so forth, and a video printer 77 for printing outvideo signals in the form of images. The video endoscope system furtherincludes a head-mounted image display apparatus (HMD) 78. The videoendoscope 71 has an insert part 79 with a distal end portion 80 and aneyepiece part 81. The distal end portion 80 and the eyepiece part 81 arearranged as shown in part (b) of FIG. 14. A light beam from the lightsource unit 72 passes through a light guide fiber bundle 88 andilluminates a part to be observed through an objective optical system 89for illumination. Light from the part to be observed enters theobjective optical system 82 for observation through a cover member 85.Thus, an object image is formed by the objective optical system 82. Theobject image is formed on the image pickup surface of a CCD 84 through afilter 83, e.g. a low-pass filter, an infrared cutoff filter, etc.Furthermore, the object image is converted into a video signal by theCCD 84. The video signal is displayed directly on the monitor 74 by thevideo processor 73, which is shown in part (a) of FIG. 14. In addition,the video signal is recorded in the VTR deck 75 and on the video disk 76and also printed out in the form of an image from the video printer 77.In addition, the object image is displayed on the image display deviceof the HMD 78, thereby allowing a person wearing the HMD 78 to observethe displayed image. At the same time, the video signal converted by theCCD 84 is displayed in the form of an electronic image on a liquidcrystal display device (LCD) 86 in the eyepiece part 81. The displayedimage is led to an observer's eyeball E through the ocular opticalsystem 87, which is formed from a viewing optical system according tothe present invention.

The endoscope arranged as stated above can be constructed with a minimalnumber of optical members. Accordingly, a high-performance and low-costendoscope can be realized. Moreover, because the constituent elements ofthe objective optical system 82 are arranged in series in the directionof the longitudinal axis of the endoscope, the above-describedadvantageous effects can be obtained without hindering the achievementof a reduction in the diameter of the endoscope.

Incidentally, the image-forming optical system can also be used as aprojection optical system by reversing the optical path. FIG. 15 is aconceptual view showing an arrangement in which a prism optical systemaccording to the present invention is used in a projection opticalsystem 96 of a presentation system formed by combining together apersonal computer 90 and a liquid crystal projector 91. In this example,an image-forming optical system similar to Example 1 except that theoptical path is reverse to that in Example 1 is used in the projectionoptical system 96. Referring to FIG. 15, image and manuscript dataprepared on the personal computer 90 is branched from a monitor outputand delivered to a processing control unit 98 in the liquid crystalprojector 91. In the processing control unit 98 of the liquid crystalprojector 91, the input data is processed and output to a liquid crystalpanel (LCP) 93. The liquid crystal panel 93 displays an imagecorresponding to the input image data. Light from a light source 92 isapplied to the liquid crystal panel 93. The amount of light transmittedby the liquid crystal panel 93 is determined by the gradation of theimage displayed on the liquid crystal panel 93. Light from the liquidcrystal panel 93 is projected on a screen 97 through a projectionoptical system 96 comprising a field lens 95 placed immediately in frontof the liquid crystal panel 93, a prism 10 constituting theimage-forming optical system according to the present invention, and acover lens 94 which is a positive lens.

The projector arranged as stated above can be constructed with a minimalnumber of optical members. Accordingly, a high-performance and low-costprojector can be realized. In addition, the projector can be constructedin a compact form.

FIG. 16 shows a desirable arrangement for the image-forming opticalsystem according to the present invention when the image-forming opticalsystem is placed in front of an image pickup device, e.g. a CCD, or afilter. In the figure, a decentered prism P is the image-side portion ofa prism member or a second prism included in the image-forming opticalsystem according to the present invention. When the image pickup surfaceC of an image pickup device forms a quadrangle as shown in the figure,it is desirable from the viewpoint of forming a beautiful image to placethe decentered prism P so that the plane F of symmetry of aplane-symmetry free-form surface provided in the decentered prism P isparallel to at least one of the sides forming the quadrangular imagepickup surface C.

When the image pickup surface C has a shape in which each of the fourinterior angles is approximately 90 degrees, such as a square or arectangle, it is desirable that the plane F of symmetry of theplane-symmetry free-form surface should be parallel to two sides of theimage pickup surface C that are parallel to each other. It is moredesirable that the plane F of symmetry should lie at the middle betweenthe two parallel sides and coincide with a position where the imagepickup surface C is in a symmetry between the right and left halves orbetween the upper and lower halves. The described arrangement enablesthe required assembly accuracy to be readily obtained when theimage-forming optical system is incorporated into an apparatus, and isuseful for mass-production.

When a plurality or all of the optical surfaces constituting thedecentered prism P, i.e. the third reflecting surface, the fourthreflecting surface, and the first exit surface, are plane-symmetryfree-form surfaces, it is desirable from the viewpoint of design andaberration correcting performance to arrange the decentered prism P sothat the planes of symmetry of the plurality or all of the opticalsurfaces are in the same plane F. In addition, it is desirable that theplane F of symmetry and the image pickup surface C should be in theabove-described relationship.

As will be clear from the foregoing description, the present inventionmakes it possible to provide a high-performance and low-costimage-forming optical system with a minimal number of constituentoptical elements. In addition, it is possible to provide ahigh-performance image-forming optical system that is made compact andthin by folding an optical path using reflecting surfaces arranged tominimize the number of reflections.

1. An image-forming optical system having positive refracting power as awhole for forming an object image, said image-forming optical systemcomprising: a first prism member formed from a medium having arefractive index (n) larger than 1 (n>1): and a second prism memberformed from a medium having a refractive index (n) larger than 1 (n>1);said first prism member comprising: a first entrance surface throughwhich a light beam from an object enters said first prism member; afirst reflecting surface and a second reflecting surface, which reflectsaid light beam within said first prism member; and a first prism exitsurface through which said light beam exits said first prism member;said second prism member comprising: a second prism entrance surfacethrough which the light beam from said first prism member enters saidsecond prism member; a third reflecting surface and a fourth reflectingsurface; and a first exit surface through which said light beam exitssaid second prism member; wherein said first prism exit surface and saidsecond prism entrance surface are positioned to face each other acrossan air spacing, wherein said first prism member forms first intersectingoptical paths in which an optical path connecting said second reflectingsurface and said first prism exit surface intersects an optical pathconnecting said first entrance surface and said first reflectingsurface, wherein said second prism member forms second intersectingoptical paths in which an optical path connecting said second prismentrance surface and said third reflecting surface intersects an opticalpath connecting said fourth reflecting surface and said first exitsurface, wherein at least one of said first reflecting surface and saidsecond reflecting surface has a curved surface configuration that givesa power to the light beam, said curved surface configuration being arotationally asymmetric surface configuration that corrects aberrationsdue to decentration, wherein at least one of said third reflectingsurface and said fourth reflecting surface has a curved surfaceconfiguration that gives a power to the light beam, said curved surfaceconfiguration being a rotationally asymmetric surface configuration thatcorrects aberrations due to decentration, wherein said first prismmember and said second prism member are arranged to form an intermediateimage plane in an optical path between said second reflecting surfaceand said third reflecting surface, and wherein said first entrancesurface has a curved surface configuration that gives a power to thelight beam, said curved surface configuration being a rotationallyasymmetric surface configuration that corrects aberrations due todecentration.
 2. An image-forming optical system having positiverefracting power as a whole for forming an object image, saidimage-forming optical system comprising: a first prism member formedfrom a medium having a refractive index (n) larger than 1 (n>1); and asecond prism member formed from a medium having a refractive index (n)larger than 1 (n>1); said first prism member comprising: a firstentrance surface through which a light beam from an object enters saidfirst prism member; a first reflecting surface and a second reflectingsurface, which reflect said light beam within said first prism member;and a first prism exit surface through which said light beam exits saidfirst prism member; said second prism member comprising: a second prismentrance surface through which the light beam from said first prismmember enters said second prism member; a third reflecting surface and afourth reflecting surface; and a first exit surface through which saidlight beam exits said second prism member, wherein said first prism exitsurface and said second prism entrance surface are positioned to faceeach other across an air spacing, wherein said first prism member formsfirst intersecting optical paths in which an optical path connectingsaid second reflecting surface and said first prism exit surfaceintersects an optical path connecting said first entrance surface andsaid first reflecting surface, wherein said second prism member formssecond intersecting optical paths in which an optical path connectingsaid second prism entrance surface and said third reflecting surfaceintersects an optical path connecting said fourth reflecting surface andsaid first exit surface, wherein at least one of said first reflectingsurface and said second reflecting surface has a curved surfaceconfiguration that gives a power to the light beam, said curved surfaceconfiguration being a rotationally asymmetric surface configuration thatcorrects aberrations due to decentration, wherein at least one of saidthird reflecting surface and said fourth reflecting surface has a curvedsurface configuration that gives a power to the light beam, said curvedsurface configuration being a rotationally asymmetric surfaceconfiguration that corrects aberrations due to decentration, whereinsaid first prism member and said second prism member are arranged toform an intermediate image plane in an optical path between said secondreflecting surface and said third reflecting surface, and wherein saidfirst exit surface has a curved surface configuration that gives a powerto the light beam, said curved surface configuration being arotationally asymmetric surface configuration that corrects aberrationsdue to decentration.
 3. An image-forming optical system according toclaim 1 or 2, wherein the rotationally asymmetric surface configurationof at least one of said first prism member and said second prism memberis a plane-symmetry free-form surface having only one plane of symmetry.4. An image-forming optical system according to claim 3, wherein the oneand only plane of symmetry of the plane-symmetry free-form surface ofsaid at least one of said first prism member and said second prismmember is coincident with a plane formed by an axial principal raytraveling along said first intersecting optical paths.
 5. Animage-forming optical system according to claim 4, wherein the one andonly plane of symmetry of the plane-symmetry free-form surface of saidat least one of said first prism member and said second prism member iscoincident with a plane formed by an axial principal ray traveling alongsaid second intersecting optical paths.
 6. An image-forming opticalsystem having positive refracting power as a whole for forming an objectimage, said image-forming optical system comprising: a first prismmember formed from a medium having a refractive index (n) larger than 1(n>1); and a second prism member formed from a medium having arefractive index (n) larger than 1 (n>1); said first prism membercomprising: a first entrance surface through which a light beam from anobject enters said first prism member; a first reflecting surface and asecond reflecting surface, which reflect said light beam within saidfirst prism member; and a first prism exit surface through which saidlight beam exits said first prism member; said second prism membercomprising: a second prism entrance surface through which the light beamfrom said first prism member enters said second prism member; a thirdreflecting surface and a fourth reflecting surface; and a first exitsurface through which said light beam exits said second prism member,wherein said first prism exit surface and said second prism entrancesurface are positioned to face each other across an air spacing, whereinsaid first prism member forms first intersecting optical paths in whichan optical path connecting said second reflecting surface and said firstprism exit surface intersects an optical path connecting said firstentrance surface and said first reflecting surface, wherein said secondprism member forms second intersecting optical paths in which an opticalpath connecting said second prism entrance surface and said thirdreflecting surface intersects an optical path connecting said fourthreflecting surface and said first exit surface, wherein at least one ofsaid first reflecting surface and said second reflecting surface has acurved surface configuration that gives a power to the light beam, saidcurved surface configuration being a rotationally asymmetric surfaceconfiguration that corrects aberrations due to decentration, wherein atleast one of said third reflecting surface and said fourth reflectingsurface has a curved surface configuration that gives a power to thelight beam, said curved surface configuration being a rotationallyasymmetric surface configuration that corrects aberrations due todecentration, wherein said first prism member and said second prismmember are arranged to form an intermediate image plane in an opticalpath between said second reflecting surface and said third reflectingsurface, and wherein optical surfaces of said first prism member thatare closer to an object side than said intermediate image plane arearranged to correct decentration aberrations as a whole and opticalsurfaces of said second prism member that are closer to animage-formation plane side than said intermediate image plane arearranged to correct decentration aberrations as a whole so that saidintermediate image plane is formed in an approximately planar shape. 7.An image-forming optical system having positive refracting power as awhole for forming an object image, said image-forming optical systemcomprising: a first prism member formed from a medium having arefractive index (n) larger than 1 (n>1); and a second prism memberformed from a medium having a refractive index (n) larger than 1 (n>1);said first prism member comprising: a first entrance surface throughwhich a light beam from an object enters said first prism member; afirst reflecting surface and a second reflecting surface, which reflectsaid light beam within said first prism member; and a first prism exitsurface through which said light beam exits said first prism member;said second prism member comprising: a second prism entrance surfacethrough which the light beam from said first prism member enters saidsecond prism member; a third reflecting surface and a fourth reflectingsurface; and a first exit surface through which said light beam exitssaid second prism member, wherein said first prism exit surface and saidsecond prism entrance surface are positioned to face each other acrossan air spacing, wherein said first prism member forms first intersectingoptical paths in which an optical path connecting said second reflectingsurface and said first prism exit surface intersects an optical pathconnecting said first entrance surface and said first reflectingsurface, wherein said second prism member forms second intersectingoptical paths in which an optical path connecting said second prismentrance surface and said third reflecting surface intersects an opticalpath connecting said fourth reflecting surface and said first exitsurface, wherein at least one of said first reflecting surface and saidsecond reflecting surface has a curved surface configuration that givesa power to the light beam, said curved surface configuration being arotationally asymmetric surface configuration that corrects aberrationsdue to decentration, wherein at least one of said third reflectingsurface and said fourth reflecting surface has a curved surfaceconfiguration that gives a power to the light beam, said curved surfaceconfiguration being a rotationally asymmetric surface configuration thatcorrects aberrations due to decentration, wherein said first prismmember and said second prism member are arranged to form an intermediateimage plane in an optical path between said second reflecting surfaceand said third reflecting surface, and wherein, when powers in X and Ydirections of an entire optical system are denoted by Px and Py,respectively, and powers in the X direction of the first reflectingsurface, the second reflecting surface, the third reflecting surface andthe fourth reflecting surface are denoted by Px1-1, Px1-2, Px2-1 andPx2-2, respectively, and further powers in the Y direction of the firstreflecting surface, the second reflecting surface, the third reflectingsurface and the fourth reflecting surface are denoted by Py1-1, Py1-2,Py2-1 and Py2-2, respectively, the following condition is satisfied:0.4<Px1-1/Px≦0.9.
 8. An image-forming optical system having positiverefracting power as a whole for forming an object image, saidimage-forming optical system comprising: a first prism member formedfrom a medium having a refractive index (n) larger than 1 (n>1); and asecond prism member formed from a medium having a refractive index (n)larger than 1 (n>1); said first prism member comprising: a firstentrance surface through which a light beam from an object enters saidfirst prism member; a first reflecting surface and a second reflectingsurface, which reflect said light beam within said first prism member;and a first prism exit surface through which said light beam exits saidfirst prism member; said second prism member comprising: a second prismentrance surface through which the light beam from said first prismmember enters said second prism member; a third reflecting surface and afourth reflecting surface; and a first exit surface through which saidlight beam exits said second prism member, wherein said first prism exitsurface and said second prism entrance surface are positioned to faceeach other across an air spacing, wherein said first prism member formsfirst intersecting optical paths in which an optical path connectingsaid second reflecting surface and said first prism exit surfaceintersects an optical path connecting said first entrance surface andsaid first reflecting surface, wherein said second prism member formssecond intersecting optical paths in which an optical path connectingsaid second prism entrance surface and said third reflecting surfaceintersects an optical path connecting said fourth reflecting surface andsaid first exit surface, wherein at least one of said first reflectingsurface and said second reflecting surface has a curved surfaceconfiguration that gives a power to the light beam, said curved surfaceconfiguration being a rotationally asymmetric surface configuration thatcorrects aberrations due to decentration, wherein at least one of saidthird reflecting surface and said fourth reflecting surface has a curvedsurface configuration that gives a power to the light beam, said curvedsurface configuration being a rotationally asymmetric surfaceconfiguration that corrects aberrations due to decentration, whereinsaid first prism member and said second prism member are arranged toform an intermediate image plane in an optical path between said secondreflecting surface and said third reflecting surface, and wherein, whenpowers in X and Y directions of an entire optical system are denoted byPx and Py, respectively, and powers in the X direction of the firstreflecting surface, the second reflecting surface, the third reflectingsurface and the fourth reflecting surface are denoted by Px1-1, Px1-2,Px2-1 and Px2-2, respectively, and further powers in the Y direction ofthe first reflecting surface, the second reflecting surface, the thirdreflecting surface and the fourth reflecting surface are denoted byPy1-1, Py1-2, Py2-1 and Py2-2, respectively, the following condition issatisfied:0.1<Px1-2/Px<0.6.
 9. An image-forming optical system having positiverefracting power as a whole for forming an object image, saidimage-forming optical system comprising: a first prism member formedfrom a medium having a refractive index (n) larger than 1 (n>1); and asecond prism member formed from a medium having a refractive index (n)larger than 1 (n>1); said first prism member comprising: a firstentrance surface through which a light beam from an object enters saidfirst prism member; a first reflecting surface and a second reflectingsurface, which reflect said light beam within said first prism member;and a first prism exit surface through which said light beam exits saidfirst prism member; said second prism member comprising: a second prismentrance surface through which the light beam from said first prismmember enters said second prism member; a third reflecting surface and afourth reflecting surface; and a first exit surface through which saidlight beam exits said second prism member, wherein said first prism exitsurface and said second prism entrance surface are positioned to faceeach other across an air spacing, wherein said first prism member formsfirst intersecting optical paths in which an optical path connectingsaid second reflecting surface and said first prism exit surfaceintersects an optical path connecting said first entrance surface andsaid first reflecting, surface, wherein said second prism member formssecond intersecting optical paths in which an optical path connectingsaid second prism entrance surface and said third reflecting surfaceintersects an optical path connecting said fourth reflecting surface andsaid first exit surface, wherein at least one of said first reflectingsurface and said second reflecting surface has a curved surfaceconfiguration that gives a power to the light beam, said curved surfaceconfiguration being a rotationally asymmetric surface configuration thatcorrects aberrations due to decentration, wherein at least one of saidthird reflecting surface and said fourth reflecting surface has a curvedsurface configuration that gives a power to the light beam, said curvedsurface configuration being a rotationally asymmetric surfaceconfiguration that corrects aberrations due to decentration, whereinsaid first prism member and said second prism member are arranged toform an intermediate image plane in an optical path between said secondreflecting surface and said third reflecting surface, and wherein, whenpowers in X and Y directions of an entire optical system are denoted byPx and Py, respectively, and powers in the X direction of the firstreflecting surface, the second reflecting surface, the third reflectingsurface and the fourth reflecting surface are denoted by Px1-1, Px1-2,Px2-1 and Px2-2, respectively, and further powers in the Y direction ofthe first reflecting surface, the second reflecting surface, the thirdreflecting surface and the fourth reflecting surface are denoted byPy1-1, Py1-2, Py2-1 and Py2-2, respectively, the following condition issatisfied:0.37≦Px2-1/Px<1.
 10. An image-forming optical system having positiverefracting power as a whole for forming an object image, saidimage-forming optical system comprising: a first prism member formedfrom a medium having a refractive index (n) larger than 1 (n>1); and asecond prism member formed from a medium having a refractive index (n)larger than 1 (n>1); said first prism member comprising: a firstentrance surface through which a light beam from an object enters saidfirst prism member; a first reflecting surface and a second reflectingsurface, which reflect said light beam within said first prism member;and a first prism exit surface through which said light beam exits saidfirst prism member; said second prism member comprising: a second prismentrance surface through which the light beam from said first prismmember enters said second prism member; a third reflecting surface and afourth reflecting surface; and a first exit surface through which saidlight beam exits said second prism member, wherein said first prism exitsurface and said second prism entrance surface are positioned to faceeach other across an air spacing, wherein said first prism member formsfirst intersecting optical paths in which an optical path connectingsaid second reflecting surface and said first prism exit surfaceintersects an optical path connecting said first entrance surface andsaid first reflecting surface, wherein said second prism member formssecond intersecting optical paths in which an optical path connectingsaid second prism entrance surface and said third reflecting surfaceintersects an optical path connecting said fourth reflecting surface andsaid first exit surface, wherein at least one of said first reflectingsurface and said second reflecting surface has a curved surfaceconfiguration that gives a power to the light beam, said curved surfaceconfiguration being a rotationally asymmetric surface configuration thatcorrects aberrations due to decentration, wherein at least one of saidthird reflecting surface and said fourth reflecting surface has a curvedsurface configuration that gives a power to the light beam, said curvedsurface configuration being a rotationally asymmetric surfaceconfiguration that corrects aberrations due to decentration, whereinsaid first prism member and said second prism member are arranged toform an intermediate image plane in an optical path between said secondreflecting surface and said third reflecting surface, and wherein, whenpowers in X and Y directions of an entire optical system are denoted byPx and Py, respectively, and powers in the X direction of the firstreflecting surface, the second reflecting surface, the third reflectingsurface and the fourth reflecting surface are denoted by Px1-1, Px1-2,Px2-1 and Px2-2, respectively, and further powers in the Y direction ofthe first reflecting surface, the second reflecting surface, the thirdreflecting surface and the fourth reflecting surface are denoted byPy1-1, Py1-2, Py2-1 and Py2-2, respectively, the following condition issatisfied:0.5<Px2-1/Py2-1<2.0.